ALBANY — Gov. David A. Paterson, buoyed by recent polls showing some modest rebounds in his approval ratings, said Thursday he will not be pushed out of a run for a full term this year — even if it means a primary race against Attorney General Andrew M. Cuomo.

“I am running for governor, and someone’s going to have to beat me,” Paterson said, dismissing what he says is an orchestrated attempt by some Democrats to get him to bow out of the race to clear the way for Cuomo.

In the past, the governor has often punted questions about facing Cuomo in a primary. And he used to add a disclaimer that he would not put his political plans above what is good for the Democratic Party.

But on Thursday, when asked if he would stand up to a Cuomo challenge, Paterson said, “I would run in a primary against anyone that’s running, because I’m running for governor and you have to get past the primary to get to the general election.”

Paterson, who recently said he is tiring of all the stories about Cuomo ruminating about a gubernatorial run, dismissed talk about a “drumbeat” of some party insiders and a union boss calling for Cuomo to quickly get into the race and Paterson to step aside.

“Drumbeats remind me of orchestras, and orchestras remind me of orchestration. So this whole idea that all these people got this idea at one time is rather hard for me to believe,” he told reporters near the Capitol. “And what I would point out is, while they’re beating their drums, I’m a drum major, and I’m working real hard, and I’m going to get this budget done, and they can do whatever they like.”

The governor has seen some improvements in his job-approval ratings, but they are still below what any politician would want to run on in the fall. In hypothetical matchups, Paterson has seen his numbers tighten with Cuomo; in November, Cuomo was beating Paterson, 75 percent to 16 percent, which changed to 59 percent to 21 percent last week, the Siena College Research Institute reported.

But Paterson trails badly in campaign dollars. Last week, he reported having just $3 million in the bank, compared with Cuomo’s $16 million. For now, Cuomo is officially running for attorney general, but Democrats say that it could be only a matter of weeks before he announces a gubernatorial challenge.

“My feeling is, this thing over the next month will crystallize a little bit,” said Erie County Democratic Chairman Leonard R. Lenihan. Unlike some Democrats, Lenihan is not publicly calling on Cuomo to jump into the race, but he left open the possibility.

“No, we’re not in that position,” Lenihan said when asked if he is looking for Cuomo to declare his candidacy now. “We’re certainly following events very closely.”

He said that most county Democratic chairmen will wait with their public recommendations until things shake out in the weeks or months ahead.

The governor said this week’s surprising victory by Republican Scott P. Brown in the U. S. Senate race in Massachusetts has not given him any pause about running this year. He said he has known of the public’s sentiment regarding incumbents since the November elections, “which is the reason why I have taken some of the approaches I’ve taken since then. I think you do have to adjust to public reaction.”

He added, “Ironically, in these same months, my approval from the public, which I usually don’t talk about, has gone up.” Also during that period, Paterson spent millions from his campaign treasury on a major advertising campaign to try to boost his poll numbers.

“If someone beats me, I’ll support the Democratic candidate,” he said of a potential primary race.

But he praised his own efforts to keep the state from slipping into financial nightmares like those affecting states such as California, while having to make unpopular spending cuts.

If he does face a Democratic primary challenge, Paterson said, “those facts will come out in that debate.”