White House press secretary Karine Jean-Pierre said US officials have contacted allies about continuing funding for Ukraine.
Ms Jean-Pierre denied suggestions that Ukraine's allies are growing weary of the war.
"There is strong, very strong international coalition behind Ukraine and if [Russian President Vladimir] Putin thinks he can outlast us, he's wrong, he's wrong," she told reporters.
"So we will have another package of aid for Ukraine soon to signal our continued support for the brave people of Ukraine."
Ms Jean-Pierre said there is enough current funding to meet battlefield needs "for a bit longer".
But it is not yet clear when Congress will introduce legislation to authorise more money for Ukraine, and debate on any measure could take weeks.
The development comes just weeks after Ukrainian President Volodymyr Zelenskyy visited Washington in a trip aimed at rallying more aid for his country.
Since Mr Putin launched an invasion of Ukraine in February last year, the US has approved about $113 billion in military and humanitarian aid to the country.
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Pentagon Comptroller Michael McCord told House and Senate leaders that there is $1.6 billion left of the $25.9 billion Congress provided to replenish US military stocks that have been flowing to Ukraine.
Military aid so far has totalled $43.9 billion in weapons, including high-profile systems such as a Patriot air defence battery and Abrams tanks, almost 200 howitzer 155mm firing systems and more than 2 million 155mm rounds, all of which are considered vital for Ukraine's war effort.
But as the war drags on, the idea of slowing US aid to Ukraine, particularly among the right-wing flank of the Republican Party, has been gaining momentum.
On Saturday, the US Congress passed a last-minute stopgap bill to avoid a government shutdown. It extended government funding for 45 days but the bill authorised no new Ukraine money.
A governmental shutdown would have cut critical services for millions of Americans and left about four million federal employees without a pay cheque.
The stopgap bill was approved with overwhelming majorities in both the House and Senate.
The US State Department on Monday urged Congress to increase security assistance funding, saying it is a matter of international security.
"While we have the ability to continue to support Ukraine's ability to defend itself in the immediate term, we have already exhausted much of the existing security assistance funding," US State Department spokesman Matthew Miller told reporters.
"It is imperative that Congress take action.
"Strong majorities in both houses of Congress support continued assistance to Ukraine because this is not simply about Ukraine, it is about the world we want to live in."
On Sunday, President Joe Biden urged Republicans in Congress to back a bill that would provide $24 billion in aid to Ukraine, and sought to reassure that there was still "overwhelming" bipartisan support on the issue.
"I hope my friends on the other side keep their word about support for Ukraine," Mr Biden said.
"I fully expect the [House] Speaker [Kevin McCarthy] to keep his commitment for the secure passage and support needed to help Ukraine as they defend themselves against aggression and brutality."