Barack Obama says his opponents are trying to "distract with smears"
US Democratic presidential nominee Barack Obama has hit back at claims by his Republican rival that he associated with "terrorists".
Mrs Palin said Senator Obama had been "palling around" with an ex-member of 1960s US-based militant group.
Mr Obama said the Republicans were out of touch and trying to distract voters from the real issues.
Alaska Governor Palin has defended the remarks, which she made several times, saying it was "fair to talk about".
At campaign stops in Colorado and California over the weekend, Mrs Palin attacked Senator Obama over his link to Bill Ayers, a founder of the Weather Underground movement.
The radical movement waged a violent campaign against the Vietnam War during the 1960s and 1970s, when Mr Obama was a child.
Mrs Palin described Mr Obama as someone who saw the US "as being so imperfect... he is palling around with terrorists who would target their own country".
In the 1990s, Mr Ayers hosted a Democrat campaign event at his home, attended by Mr Obama.
Mr Obama accused the McCain campaign of engaging in "swift boat" politics - a reference to a campaign of attacks on John Kerry's military record during the 2004 presidential campaign.
'Out of ideas'
Mr Obama once served on a charity board with Mr Ayers but the White House hopeful has denied having any close association with him or his views and has denounced the Weather Underground group.
Mrs Palin said the issue was fair to talk about
He has described Ms Palin's comments as offensive and false.
The Illinois senator told his supporters at a rally in North Carolina that John McCain was "gambling that he can distract you with smears rather than talk to you about substance".
"They'd rather tear our campaign down than lift this country up," he said.
"That's what you do when you're out of touch, out of ideas, and running out of time."
The party has accused the Republicans of gutter politics.
Ohio Senator Sherrod Brown said that the last few weeks had seen Mr McCain "morph into a desperate angry candidate" and that it made him sad that the McCain campaign was "resorting to these tactics".
Commentators say Mrs Palin's attack forms part of a broader Republican strategy to attack Mr Obama's character.
The Obama campaign responded with a new advertisement, which will air nationally on cable TV stations, claiming Mr McCain has behaved erratically during the Wall Street meltdown.
The commercial says Mr McCain is attacking Mr Obama personally to distract voter attention from the loss of 750,000 American jobs this year and continuing financial turmoil.
"And John McCain?" the advertisement asks, before answering: "Erratic in a crisis. Out of touch on the economy."
Mrs Palin has defended her comments, saying they were "about an association that has been known but hasn't been talked about".
"I think it's fair to talk about where Barack Obama kicked off his political career, in the guy's living room."
Minnesota Governor Tim Pawlenty, a Republican, said the issue was a test of Mr Obama's character.
"It goes to the issue of what kind of judgment would allow an unrepentant domestic terrorist to host a political event for you in his home," he told ABC News.
The row has dominated the media over the weekend and came ahead of a Monday deadline for voters to register in more than a dozen states, including Pennsylvania, Michigan, Ohio, Indiana and Florida.
The latest polls put Barack Obama ahead of John McCain but voter turnout could be vital in deciding the outcome of the 4 November presidential election.
The BBC's Rajini Vaidyanathan in Washington says that with a month to go until polling, the politics on both sides are expected to get much more personal.