Senator Clinton is risking a clash with the liberal blogosphere by agreeing to a debate proposed by Fox News, a network which was denied two Democratic presidential candidates debates last year by elements in the party angry at what they perceive as Fox’s right-wing tilt.

“It was a good offer and we took it,” a top adviser to Mrs. Clinton, Howard Wolfson, told reporters in a conference call this afternoon. “I hope that Senator Obama follows up by accepting.”

Mr. Wolfson said the Fox-sponsored exchange, which would take place in Washington D.C. on February 11, would be carried live on the city’s Fox affiliate and therefore represents an opportunity to reach voters from Maryland and the capital taking part in the so-called Potomac Primary the following day.

“It makes sense in terms of viewership,” he said.

In March, outrage from liberal Web commentators, often called the netroots, led to the cancellation of a debate Fox planned to hold August 14 in Reno, Nev. Officially, the Nevada Democratic Party withdrew backing for the debate over joking comments Fox’s chairman, Roger Ailes, made comparing Mr. Obama to Osama bin Laden. A September session to be co-sponsored by Fox and the Congressional Black Caucus foundered for similar reasons.

A candidate who was aggressively courting the so-called netroots and who has since dropped out, John Edwards, was the first to announce he would skip the debates. Mr. Obama and Mrs. Clinton soon followed.

The notion of Fox-sponsored Democratic debates was already under fire from the party’s left flank, which regards Fox as a part of a sinister empire of conservative media outlets under the control of News Corporation chief, Rupert Murdoch.

The backlash over the proposed Fox debate next week began on Mr. Wolfson’s call with reporters when a prominent liberal blogger, Jane Hamsher of Firedoglake.com, asked the strategist if attending such a debate would “legitimize” Fox.

“It’s my understanding that Senator Obama has appeared on Fox recently more than once, so that’s a decision that they have made presumably to appear on the network,” Mr. Wolfson said. He acknowledged that Mrs. Clinton has also done a series of interviews with Fox.

The answer did not satisfy Ms. Hamsher. “Fox is not a news outlet, it’s an openly partisan opinion factory and the Democrats should not be legitimizing them (and allowing them to recruit Democratic viewers to propagandize to) by doing this,” she wrote in a Web post moments later.

Last week, one of the liberal groups that urged a boycott of the Fox debates, Moveon.org, endorsed Mr. Obama. The Clinton campaign’s decision to go forward with a Fox debate may reflect a conclusion that inflaming the netroots is now of little consequence to her campaign because Mr. Obama has won the allegiances of the majority of liberal Web activists.

Asked if the Moveon.org endorsement affected the decision to accept the Fox debate, Mr. Wolfson said it was not the only group that objected to the now-scuttled sessions in August and September, but he also acknowledged the anger those proposals generated. “It was more than just Moveon. It was something that the progressive blogosphere felt strongly about, too.”

In response to a question from The New York Sun about whether the acceptance of the Fox debate signaled that Mrs. Clinton was effectively giving up on the left-wing and looking for centrist voters, Mr. Wolfson said, “No. Look, we have a large and diverse party. We’re going to continue reaching out and talking to all parts of the party.”

When the issue of Fox debates arose last year, Mr. Edwards bluntly accused the network of bias and Mr. Obama’s campaign said CNN would be a better host for the September session. Mrs. Clinton’s campaign was more vague about her reasons for rejecting last year’s offers by Fox.

Mr. Murdoch hosted a fund-raiser for Mrs. Clinton last year, but one of his major newspapers, the New York Post, recently endorsed Mr. Obama.

There was no immediate word from Mr. Obama’s campaign about whether he planned attend the proposed February 11 exchange or three other debates Mrs. Clinton’s camp agreed to yesterday: a February 10 debate on ABC’s “This Week,” a February 27 debate in Ohio on CNN, and a February 28 debate in Texas moderated by an MSNBC host who has had a difficult relationship with Mrs. Clinton, Chris Matthews.

A spokesman for Mr. Obama, Bill Burton, said the campaign would decide “soon” on the candidate’s schedule for debates and other events.

The Clinton campaign’s offer of four debates in coming weeks seemed to underscore the view of Mrs. Clinton’s aides that she performs well in policy discussions. The debate offers also send the message that the Democratic contest will continue past tonight, even if Mr. Obama wins more delegates.