The race for the White House remained a dead heat following this year's first debate between President Joe Biden and former President Donald Trump, according to a new poll.

But fewer likely voters said they felt Biden was mentally fit to be president following his dismal performance, the Ipsos polling company reported online Saturday.

And a focus group of undecided voters immediately after the Thursday night debate showed that while they thought Biden clearly lost the face-off, Trump didn't necessarily win it, Ipsos noted.

The two-wave, Ipsos/538 poll was conducted on Wednesday and Thursday and showed 44% of respondents said they were considering voting for Biden before the debate and 46% said they were considering doing so afterward.

Trump's likely support was also 44% before the debate but was unchanged afterward, Ipsos said.

Likely support for independent candidate Robert F. Kennedy Jr. was also unchanged at 18% before and after the debate, for which he failed to qualify.

The margin of error among all respondents was 2.1% and the margin among those who watched all or part of the debate was 2.5%.

Before the debate, 27% of likely voters rated Biden's mental fitness to be president as "good" or "excellent," but that figure plunged to 20% afterward, Ipsos said.

The decline was steepest among Democrats, who went from 56% before the debate to 42% after.

Trump's positive mental fitness ratings rose slightly after the debate, from 39% to 41%, a change that's within the margin of error.

A 90-minute, post-debate focus group discussion with six undecided voters in Chicago showed they were "disillusioned with both candidates, citing poor performances that failed to address key issues," Ipsos said.

"Biden's health was a concern for many, as was Trump's narcissism," Ispos said.

"Neither candidate was able to exceed expectations, leading many to express frustration and disappointment, and some respondents indicating they might be less likely to vote at all." 

A CBS News/You Gov poll after the debate out Sunday found that 72% of Americans don't believe Biden has the "mental and cognitive health to serve as president." That's a 7 point increase from just three weeks ago. 

Nearly half of registered voters polled in Biden's own party, 45%, said the president should not run. 

Voters were essentially split on whether former Trump has the mental and cognitive health for the job, with 50% saying he does, and 49% saying he doesn't.

A separate Data for Progress post-debate flash poll found that 57% of voters surveyes believe Biden is too old to run for president (35% believe Trump is too old), but that alternative Democratic candidates would currently do no better against Trump. 

While that poll found Biden (45%) trailing Trump (48%) among respondents, all other leading Democratic figures would perform the same or worse in a head-to-head match-up. 

Possible alternative candidates include Vice President Kamala Harris (45-48), California Gov. Gavin Newsom (44-47) and Michigan Gov. Gretchen Whitmer (44-46).