Volodymyr Zelensky was due to meet the US president at the White House on Thursday, as a row with Donald Trump and the broader Republican party escalated.
Republicans in Congress reacted angrily to the Ukrainian president's decision to visit an arms factory in Biden's hometown of Scranton with several top Democrats, and it now appears Zelensky will not meet Trump as had been expected.
Zelensky will pitch a "victory plan" to Joe Biden and Vice-President Kamala Harris which he says will help force Russia to find a diplomatic end to the war.
Earlier, Biden announced a $7.9bn (£5.9bn) package of military assistance to Ukraine.
Zelensky's visit with several top Democrats to an ammunition factory in the key swing state of Pennsylvania has widely angered leading Republicans, who labelled it a partisan campaign event.
In a public letter, speaker of the US House Mike Johnson said the visit was "designed to help Democrats" and claimed it amounted to "election interference".
He also demanded that Ukraine fire its ambassador to Washington who helped arrange the visit.
The Republican-led House Oversight Committee has also announced it would investigate whether Zelensky's trip was an attempt to use a foreign leader to benefit Vice-President Kamala Harris's campaign.
Her Republican rival for the presidency, Donald Trump, mocked Zelensky at a campaign event as the "greatest salesman on Earth" and accused him of refusing to "make a deal" with Moscow.
During an earlier rally on Tuesday, Trump also praised Russia's military capabilities, saying: "They beat Hitler, they beat Napoleon - that’s what they do, they fight."
The two men have long had a fractious relationship. In 2019, Trump was impeached by the US House over accusations that he pressured Ukraine's leader to dig up damaging information on a political rival.
The row clouded a week in which Zelensky has twice addressed the United Nations, ramping up efforts to persuade the US and other allies to boost support more than two and a half years into Russia's full-scale invasion.
His so-called victory plan has so far been kept under wraps, although he has described it as a "bridge" towards stopping the war that has to be agreed and put into action in the next three months.
Zelensky also needs US backing to fire Western-made long-range missiles deep into Russian territory, which Biden has so far blocked.
On the eve of the White House meeting, Russia's Vladimir Putin announced a plan to revise Moscow's nuclear doctrine, to enable Russia to use nuclear weapons against non-nuclear states if they are supported by nuclear states.
Putin's spokesperson later clarified that it was meant as a "specific signal" to the West.
Hours before his meeting with Zelensky, President Biden announced a "surge in security assistance for Ukraine and a series of additional actions to help Ukraine win this war".
The aid, part of a $61bn package that passed Congress in April, will be approved through presidential drawdown authority and will pull from existing Pentagon supplies to deliver the arms more quickly.
Congressional Republicans blocked the package for months earlier this year, before ultimately relenting and passing the legislation. The delay caused arms supplies to Ukraine to dry up for several months.
Responding to the aid package, Zelensky thanked the US - Ukraine's largest foreign donor - and said he was "grateful to Joe Biden, US Congress and its both parties".
Russia's missile and drone attacks on Ukraine have continued while Zelensky is in the US.
The Sumy, Odesa and Kyiv regions were all attacked overnight, leaving one woman dead in Odesa and numerous reported injuries.
In the capital, air raid sirens and explosions from Ukraine's air defences continued for hours.