KRUN, Germany — Four months into Russia’s invasion, unprecedented Western economic retaliation and military aid to Ukraine have not curbed Vladimir V. Putin’s ability or apparent determination to wage war, leaving leaders of the world’s wealthiest democracies grasping for new ways to deter him.
Meeting on Monday in the Bavarian Alps, President Biden and the other Group of 7 leaders were poised to embrace an aggressive but untried plan to manipulate the price of oil and restrict the revenue that underwrites Mr. Putin’s war machine.
Even as they searched for different tactics to hinder Moscow, Russia launched a barrage of missiles deep into Ukraine, striking civilian targets including, Ukrainian officials said, a crowded shopping mall where at least 13 people were killed. In a statement condemning that strike, the G7 leaders said: “Indiscriminate attacks on innocent civilians constitute a war crime. Russian President Putin and those responsible will be held to account.”
Allied leaders had hoped that economic sanctions would damage the Russian economy so severely and quickly that Mr. Putin would face economic and political pressure to cut short the war. Instead, Russian oil revenue remains high, internal opposition has been muzzled and, as Mr. Putin gloats, it is the West that is suffering high fuel prices that risk domestic political backlash.
Russia will no doubt suffer more over time — its economy will shrink by nearly 10 percent this year, economists predict, and a European Union embargo on most imports of Russian oil will take effect in December. But as Ukraine and Russia know all too well, every day counts in a war of attrition.
Administration officials said on Monday that Mr. Biden would send advanced antiaircraft systems to Ukraine, and NATO announced plans to raise the number of troops stationed in Eastern Europe and vastly increase the troops ready for rapid deployment.
But the most novel — and, administration officials said, possibly the most consequential — move came from the G7 meeting, where leaders were nearing an agreement in principle to adopt price caps on Russian oil, restricting the cash flow to the Kremlin.
Despite the sanctions imposed so far, Russian oil revenue has grown this year along with soaring fuel prices, while consumers around the world have faced mounting pain at the gasoline pump. As Russia’s sales to the West have dropped, its sales to China and India have grown.
The United States has banned Russian oil imports, but they were small, and the embargo by Europe, historically Russia’s biggest customer, has not yet taken effect. Any price caps would not interfere with those bans.
A price cap would allow Russia to keep selling oil abroad but sharply limit its revenue. It is the brainchild of Janet L. Yellen, Mr. Biden’s Treasury secretary, who has told world leaders in recent weeks that such a cap would be the best way to reduce oil prices and avert a global recession.
The details are likely weeks or more away from completion, requiring intense negotiations by G7 finance ministers, private companies and leaders of countries in Latin America, Africa and elsewhere that buy Russian oil. There is no guarantee that the plan will come together quickly, or at all, or that it will succeed as the G7 leaders hope.
On Sunday, the G7 leaders said they were banning imports of Russian gold, another sign that the West is looking for new ways to isolate Moscow financially.
Read More About Oil and Gas Prices
The G7 nations “are steadfast in our solidarity with Ukraine,” Mr. Biden and his fellow leaders said in a written statement on Monday, “and reaffirm our unwavering commitment to support the government and people of Ukraine in their courageous defense of their country’s sovereignty and territorial integrity.”
Mr. Biden did not speak to cameras or reporters on Monday, keeping an unusually low profile at the summit. His national security adviser, Jake Sullivan, told reporters that President Volodymyr Zelensky of Ukraine, speaking by video link, had told the G7 leaders that “he believes that a grinding conflict is not in the interest of the Ukrainian people, for obvious reasons.”
“So he would like to see his military and those in the West who are supporting his military make maximum use of the next few months,” Mr. Sullivan said, “to put the Ukrainians in as good a position as they can possibly be in with respect to the situation on the ground.”
But events outside the Alps underscored how Mr. Putin still holds a strong hand, with Russian energy revenue running at roughly $1 billion a day, allowing him to raise pensions and wages at home while keeping up a war effort that has broadened in recent days.
On Monday, Moscow pushed forward with slow but steady gains in Ukraine’s east, with both sides suffering heavy casualties, while maintaining persistent shelling of cities throughout Ukraine.
In Kremenchuk, a city far from the front lines in central Ukraine, an explosion reduced a shopping center to a flaming, partly collapsed ruin, and officials said it had been struck by a Russian missile. They said at least 13 people were dead, 10 missing and 25 hospitalized.
The mall had “no strategic value,” Mr. Zelensky wrote on Telegram. “Only the attempt of people to live a normal life, which so angers the occupiers.”
Northeast in the city of Kharkiv, a missile strike killed four people and injured 19, including four children, according to the regional governor, Oleg Synegubov. He wrote on Telegram, “The enemy deliberately terrorizes the civilian population.”
The strikes came a day after missiles rained on Kyiv, the capital.
Mr. Zelensky’s first request to G7 leaders on Monday was for antiaircraft systems to defend against cruise missiles, Mr. Sullivan said, and Mr. Biden “was able to be positively responsive to him on that.”
Officials said the United States would supply Ukraine a NASAMS — an advanced, medium-to-long-range surface-to-air missile defense system. Mr. Sullivan said the administration would also send more ammunition for artillery and counter-battery radar systems.
In Brussels, Jens Stoltenberg, the NATO secretary general, said member nations would increase the troops kept “on standby,” meaning ready for rapid deployment, more than sevenfold, from 40,000 to 300,000, and would sharply increase the number stationed in countries bordering Russia and its ally, Belarus.
The announcement came ahead of a NATO summit to begin Tuesday, where the alliance is expected to update its strategic mission statement for the first time in 12 years, identifying Russia as an adversary rather than a potential partner, and China as a possible threat.
Mr. Biden has pressed his counterparts to support the oil price cap plan floated by Ms. Yellen, and European leaders have warmed to the idea as they have grown to understand how it might work in concept.
Ms. Yellen is an economist by training, and her idea rests on an economist’s logic: that countries will seek to pay as little as possible for a crucial commodity like oil, regardless where their leaders stand on the Ukraine war.
It also rests on an idea that might seem jarring to anyone who watched Mr. Biden and allies target Russian oil exports soon after the invasion. Instead of seeking to drive Russian oil off the world market, the price cap would try to keep Moscow’s oil exports flowing — but at a cut rate.
With a price cap, American officials hope to leverage the fact that Western banking, insurance and shipping companies facilitate much of Russia’s oil exports — and to use those industries as a choke point to drive down the price of Russian oil.
There are several ways a cap might work, but under any of them, certain countries would continue to buy oil from Russia, but only at a price far below global market value. Administration officials believe that China and India could very likely insist on paying a similarly low rate — lower than the discount they are currently enjoying — out of sheer economic self-interest.
Ideally, officials say privately, that chain of events could convince oil traders that global oil supply volume will not face disruption when Europe’s import ban ramps up in the months ahead, a development that could push down prices.
That calculation could be wrong. Russia could decide to sell less oil if the price is kept low, though administration officials say it would be expensive for Russian oil producers to cap their wells.
There is also the political risk, in Europe and possibly the United States, if consumers grow angry that Chinese and Indian consumers can buy Russian oil at a discount.
For Europe, which is bracing for a financial hit from the decision to phase out most Russian oil imports by year’s end, an oil price cap could be good policy but hard politics.
If G7 leaders approve the policy, applying it will be painstaking, politically fraught and time-consuming, European officials warned on Monday. Reaching consensus in Europe to endorse an oil embargo nearly broke the bloc’s unity against Russia; European Union officials and diplomats cautioned that reopening that debate to introduce the price cap could face resistance by a number of E.U. countries.
A final agreement would also require complex discussions that would likely need to include private companies, like insurers and large financial firms, along with countries outside Europe and the United States that import oil from Russia.
American officials said negotiators could work out details, with the G7 leaders’ blessing, though they declined to give an exact timeline.
“I think it can be done relatively quickly,” Mr. Sullivan said.
Reporting was contributed by Richard Pérez-Peña from New York, Valerie Hopkins from Kremenchuk, Ukraine, Michael D. Shear from Madrid, Matina Stevis-Gridneff and Steven Erlanger from Brussels, Anton Troianovski from Paris and Ivan Nechepurenko from Tbilisi, Georgia.