A senior US official told reporters that negotiations on how to cap the amount of money the Russians can get for their key oil exports were advancing.
"We're still in final discussions with other G7 counterparts working to finalize this, but we're very close to a place where G7 leaders will have decided to urgently direct relevant ministers to develop mechanisms to set a global price cap for Russian oil," the official told reporters, speaking on condition of anonymity.
The goal of the plan is to starve the Kremlin of its "main source of cash and force down the price of Russian oil".
The White House also unveiled new measures to hamper Russia's ability to resupply the weaponry used in its onslaught against neighboring Ukraine.
"G7 leaders will align and expand targeted sanctions to further restrict Russia's access" to Western technology that can support the Russian arms industry, the White House said.
And the US will also "aggressively target Russian defense supply chains... and limit Russia's ability to replace the military equipment it has already lost during its brutal war".
In another measure meant to punish President Vladimir Putin's Russia and increase assistance to pro-Western Ukraine, the G7 plans to turn funds raised in recently imposed trade tariffs on Russian exports into assistance for Ukraine.
President Joe Biden and other G7 leaders "will seek authority to use revenues collected by any new tariffs on Russian goods to help Ukraine and to ensure that Russia pays for the cost of its war", the senior US official told reporters.
The idea of price capping Russian oil -- and also gas -- has support from Italy and also France.
It would work by countries continuing to import the energy they need from Russia but refusing to pay above a set price. This would, in theory, reduce inflation pressures back home while cutting into Russian profits.
The calculation is that Moscow would have no alternative but to agree, because it badly needs the revenues.
The French presidency has however said the measure would be "much more powerful if it came from the producing countries", and that it was necessary to work with OPEC+ and other oil producers around the world.
The United States and Canada, which are far less reliant on Russia as an energy supplier, have banned all Russian oil imports.