When Mr. Romney arrived in New Hampshire to deliver an afternoon speech, he struck a subdued tone. Asked by reporters why Mr. Gingrich seemed to be doing well, he suggested that his rise might be only temporary and included Mr. Gingrich’s name with a string of Republicans whose stars have risen and later fallen, like Herman Cain and Donald Trump.

“I think people are taking a very careful look, because we are very, very committed as a conservative group of voters, that we want someone we can nominate who will both beat Barack Obama and fix the country,” Mr. Romney said. He added, “Sometimes they like what they see; sometimes after they’ve examined it for a while the numbers come down a bit.”

But advisers to Mr. Romney are taking Mr. Gingrich seriously and trying to determine how to raise questions about his candidacy that may resonate in the minds of voters. The Romney campaign unleashed a forceful barrage of attacks last week, and aides said a similar pattern was expected in the coming days.

New television advertisements against Mr. Gingrich are ready to be broadcast this week by the Romney campaign. But aides said they were weighing how aggressively to go after Mr. Gingrich. The campaign is also taking steps to urge Republican leaders to keep raising doubts about Mr. Gingrich, a former House speaker.

The strategy is complicated by the fact that the rest of the Republican candidates are also sharpening their distinctions with Mr. Romney and Mr. Gingrich in an effort to raise doubts about both men in the eyes of conservative voters.

Representative Ron Paul of Texas, who has a strong organization and a loyal following in Iowa, said Sunday that there was little difference between Mr. Romney and Mr. Gingrich.

“I think they come from the same mold,” Mr. Paul said in an interview on NBC’s “Meet the Press.” “They’re both on the defensive. They’re both explaining themselves.”

Representative Michele Bachmann of Minnesota said Sunday that “there’s not a dime’s worth of difference between the two of them.” In an appearance on CBS News’s “Face the Nation,” she repeated a phrase she coined at the debate, “Newt Romney,” and urged voters to study the health care records of the men, noting that both “have advocated for a health care mandate.”