Biden and Trump each had 40 per cent support among registered voters in the two-day poll that concluded on Tuesday.
A previous Reuters/Ipsos poll conducted on June 11-12 showed Trump with a marginal two percentage-point lead, 41 per cent to 39 per cent.
The two faced off in a televised debate last Thursday, where Biden stammered throughout and failed to challenge Trump's attacks.
The new Reuters/Ipsos poll also showed that, following the debate, about one-in-three Democrats think Biden should drop out of the race, something he has pledged not to do.
The poll, which gathered responses online and nationwide from 1070 US adults, had a 3.5 percentage point margin of error for registered voters, many of whom remain on the fence with about four months left before the November 5 election.
One in five registered voters said that they were not sure for whom to vote, that they would pick a different candidate or that they would not vote at all.
The latest poll did not include a question on support for independent candidate Robert Kennedy Jr.
The June poll found 10 per cent of registered voters would back him if he appeared on the ballot.
While nationwide surveys give important signals on American support for political candidates, just a handful of competitive states typically tilt the balance in the US electoral college, which ultimately decides who wins a presidential election.
Both candidates carry significant liabilities. For Biden, these include concerns about his age - 81 - that were magnified by his debate performance.
The latest Reuters/Ipsos poll found 83 per cent of Democrats and 97 per cent of Republicans agreed with a statement that "Biden stumbled and appeared to show his age" in the debate.
Only 58 per cent of Democrats and 11 per cent of Republicans had the same assessment of Trump's debate performance.
Trump, 78, in May became the first US president to be convicted of a crime, whether in office or after leaving the White House.
He is scheduled to be sentenced in September and faces potential prison time after a jury found him guilty of 34 charges stemming from a hush money payment to an adult film actress before the 2016 presidential election.
