MANCHESTER, N.H. — Senator Hillary Rodham Clinton of New York rode a wave of female support to victory over Senator Barack Obama in the New Hampshire primary on Tuesday night. In the Republican primary, meanwhile, Senator John McCain of Arizona revived his presidential bid with a Lazarus-like win.

Both candidates called their victories comebacks, because both followed their defeats in the Iowa caucuses, where Mrs. Clinton placed third and Mr. McCain fourth.

Mr. McCain’s victory was the fruit of a meticulous and dogged turnaround effort; his second bid for the White House was in tatters last summer because of weak fund-raising and a blurred political message, leading him to fire senior advisers and refocus his energy on New Hampshire.

Mrs. Clinton’s victory came after her advisers had lowered expectations with talk of missteps in strategy and concern about Mr. Obama’s momentum coming out of the Iowa caucuses.

Mrs. Clinton told supporters, “I want especially to thank New Hampshire. Over the last week I listened to you and in the process I found my own voice.”

She added, “Together, let’s give America the kind of comeback New Hampshire has just given me.’

Mr. Obama conceded the race to Mrs. Clinton, congratulating her on a “hard-fought victory.”

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Several New Hampshire women, some of them undecided until Tuesday, said in interviews that a galvanizing moment in the race had been Mrs. Clinton’s unusual display of emotion on Monday when her eyes filled with tears and her voice cracked as she described the pressures of the race and her goals for the nation.

“As voters began to see the choice they have and heard Hillary speak from her heart, they came back to her,” said Mark Penn, Mrs. Clinton’s chief strategist.

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