OLYMPIA, Wash. – Democrat Christine Gregoire, winner of one of the closest governor’s races in American history, was inaugurated yesterday amid a legal challenge that could undo her election.

A roar of approval went up from fellow Democrats as Ms. Gregoire raised her hand and took the oath of office before a joint session of the Democrat controlled Legislature.

Republicans, who had battled unsuccessfully to delay her inauguration, gave her a frosty reception. During her 45-minute speech, they mostly sat in stony silence, remaining in their chairs during several standing ovations.

“This is not an easy time to lead,” said Ms. Gregoire, a scrappy three-term attorney general who fought the tobacco industry. “Many have asked how I can govern without a clear mandate from the voters. I believe the voters have given all of us a mandate – a mandate to overcome our differences and to solve problems.”

Backers of her Republican rival, Dino Rossi, continue to push for a whole new election to decide the race.

Mr. Rossi watched the ceremony on television at his “Rossi Revote Headquarters,” and said, “Most people believe that Washington does not have a legitimately elected governor.”

Although the state is dependably Democratic, Ms. Gregoire lost the first count in the November 2 election by 261 votes and a machine recount by 42 votes. But she pulled ahead in a final hand recount ordered by Democrats, winning by just 129 votes out of 2.9 million ballots cast.

Ever since Mr. Rossi lost the hand recount, Republicans have said widespread irregularities, including votes cast by felons and dead people, spoiled the election to the point where it is impossible to truly know who won.

Republicans also point to the admission of officials in King County, a Democratic stronghold and the state’s largest county, that they cannot match more than a thousand votes to actual voter names.

Invoking a rarely used law that allows an election “contest,” Republicans have asked the courts to set aside the election and order a revote.

The case is expected to end up in the state Supreme Court.

One sign of how unsettled the race remains is the $730,000 Democrats paid for the hand recount, which is supposed to be refunded when the count reverses the results of the election. Secretary of State Samuel Reed is holding on to the deposit until the courts rule.

Ms. Gregoire didn’t apologize or acknowledge the continuing legal battle, but in a late insert to her prepared speech, she reached out to Mr. Rossi.

“Trust me, there is no one in the state of Washington who knows how grueling the campaign has been, and the two recounts, than my husband and our two daughters,” Ms. Gregoire said. “So my heart goes out, my sincere appreciation and thanks, go out to Senator Rossi and his family for all they have done and the personal commitment they have made on behalf of the citizens of the state of Washington.”

Ms. Gregoire, 57, said the state is more unified than might be apparent from the disputed election. Voters everywhere want good-paying jobs, affordable health care, efficient government, good schools, and a clean environment, she said. She also announced the creation of a commission to look at election reform.

Meanwhile, a new judge was assigned yesterday to Mr. Rossi’s election challenge. Franklin County, which like all Washington counties is being sued by Mr. Rossi, objected to Chelan County Superior Court Judge T.W. Smalls, but did not give a reason. A preliminary hearing was scheduled for January 20; it will deal mostly with scheduling, not the underlying issues.