Four months into Russia’s invasion, unprecedented Western economic retaliation and military aid to Ukraine have not dampened Vladimir V. Putin’s ability or apparent determination to wage war, leaving leaders of the world’s wealthiest democracies scrambling for new deterrents.

President Biden and the other Group of 7 leaders were set to embrace an aggressive but untested plan on Monday in the Bavarian Alps to manipulate the price of oil and limit the revenue that underpins Mr. Putin’s war machine.

Despite their efforts to find new ways to thwart Moscow, Russia launched a barrage of missiles deep into Ukraine, striking civilian targets including, according to Ukrainian officials, a crowded shopping mall where at least 13 people were killed. The G7 leaders said in a statement condemning the strike, “Indiscriminate attacks on innocent civilians constitute a war crime.” Russian President Putin and those responsible will face consequences.”

Economic sanctions, Allied leaders hoped, would damage the Russian economy so severely and quickly that Mr. Putin would face economic and political pressure to end 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 from high fuel prices, which could lead to domestic political backlash.

Russia will undoubtedly suffer more in the long run; economists predict that its economy will contract by nearly 10% this year, and a European Union embargo on most Russian oil imports will go into effect in December. But, as Ukraine and Russia have discovered, every day counts in an attrition war.

Mr. Biden, according to administration officials, will send advanced antiaircraft systems to Ukraine, while NATO announced plans to increase the number of troops stationed in Eastern Europe and vastly increase the number of troops ready for rapid deployment.

But the most novel — and, according to administration officials, potentially most consequential — move came from the G7 meeting, where leaders were close to reaching an agreement in principle to impose price caps on Russian oil, limiting cash flow to the Kremlin.

Despite the sanctions imposed thus far, Russian oil revenue has increased this year, despite rising fuel prices, while consumers around the world have felt increasing pain at the pump. Russia’s sales to the West have decreased, while sales to China and India have increased.

The US has banned Russian oil imports, but they were small, and Europe’s embargo, historically Russia’s largest customer, has yet to take effect. Price caps would not conflict with those bans.

A price cap would allow Russia to continue selling oil abroad while severely limiting its revenue. It is the idea of Janet L. Yellen, Mr. Biden’s Treasury Secretary, who has recently told world leaders that such a cap would be the best way to reduce oil prices and avoid a global recession.

Officials said the US would provide Ukraine with a NASAMS, a medium-to-long-range surface-to-air missile defense system. Mr. Sullivan added that the administration would also send more artillery ammunition and counter-battery radar systems.

NATO Secretary General Jens Stoltenberg announced in Brussels that member nations would more than sevenfold the number of troops kept “on standby,” meaning ready for rapid deployment, 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 set to begin on Tuesday, where the alliance is expected to update its strategic mission statement for the first time in 12 years, naming Russia as an adversary rather than a potential partner and China as a potential threat. 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.