ALBANY – Governor Pataki says he might run for a fourth term in 2006 but won’t make the decision until sometime next year.

In an interview yesterday with the Associated Press, the Republican governor did not rule out challenging Senator Clinton at the end of her term, also in 2006, but hinted that the job does not appeal to him. “I enjoy very much being an executive,” he said.

His comments come one week after Attorney General Eliot Spitzer formally announced that he is running for governor, making him the front-runner for the Democratic nomination. If Mr. Pataki has been hoping for a spot in the second Bush administration – which he has repeatedly denied – his chances are declining with each vacancy that the president fills.

Political observers said this leaves Mr. Pataki little realistic choice but to stay in Albany, especially if he harbors an ambition to seek the White House in 2008.

“I love this job and there’s a lot left to do,” Mr. Pataki told the AP. “I will run again if there are things that I can do for the people of New York that build on the efforts we’ve made thus far, that others can’t do.”

He said he would make the decision after next year’s legislative session. With the state facing a $6 billion budget deficit and other knotty problems, the session is likely to last deep into the summer.

One Republican activist, speaking on condition of anonymity, said there is a serious possibility Mr. Pataki will opt for seeking re-election.

“He has nowhere else to go,” the activist said. “He wants to run for president, but it’s better for him to run for president as the governor than as the ex-governor. … His window of opportunity for other positions is closing every day as new appointments are announced by the White House.”

This activist said the governor’s aides have been putting out the word that Mr. Pataki is in contention for various federal jobs – administrator of the Environmental Protection Agency, secretary of homeland security, ambassador to the U.N.- even as the governor himself has insisted he has no interest.

In his AP interview, Mr. Pataki again denied that he was seeking a Cabinet post. “God, how many times do I have to say it?” he said.

Although Mr. Pataki has never lost a general election in his 24-year political career, the 2006 election at this point looks like an uphill battle. The only governor to win four terms in modern history is Governor Rockefeller, a Republican who left in the middle of his last term to become vice president. When Governor Cuomo, a Democrat, tried to duplicate Mr. Rockefeller’s feat, he narrowly lost to Mr. Pataki in 1994.

Mr. Pataki himself pledged during the 1994 campaign to serve no more than two terms but changed his mind after the terrorist attacks of September 11, 2001.

Speaking at the 92nd Street Y last month, two of Mr. Pataki’s allies, Mayor Koch and Senator D’Amato, urged him not to run, saying he “should know when to get off the stage.” A poll released last week by Quinnipiac University shows the governor losing to Mr. Spitzer by 12 points; it shows him losing to Mrs. Clinton by 14 points.

Also yesterday, Mr. Pataki announced he will spend most of the rest of December on vacation in Central Europe, which would seem to rule out any chance that the Legislature will reconvene this year.

Mr. Pataki called it “just a family trip.”

“We rarely get a chance to have the entire family together,” he said.

The Republican majority leader of the Senate, Joseph Bruno, said last week that he still hopes pass an overhaul of the chronically gridlocked budget process by the end of the month. But the Democratic speaker of the Assembly, Sheldon Silver, said there was no reason not to deal with the issue in January.

Once the New Year arrives, the Legislature loses its chance to override Mr. Pataki’s veto of the budget reform proposal that both houses unanimously approved in June.

A supporter of the proposal, Blair Horner of the New York Public Interest Research Group, said it is inconsistent for lawmakers to tout their budget reform plan during the campaign season and then allow the governor’s subsequent veto to go unchallenged.

“They’ve made a pledge to the public that they should not break,” Mr. Horner said. “And just as a political tactic, however this plays out, they are weakening their own hand unless they show they can act.”

A spokesman for the Assembly, Charles Carrier, said nothing is lost by taking more time to negotiate a compromise with the governor because the accompanying constitutional amendment, which must be approved by voters, cannot take effect until 2006.

“The speaker felt that the time provided for these discussions could move into next year without compromising anything,” Mr. Carrier said.

An official involved in the negotiations, speaking on condition of anonymity, said they were progressing “slowly, painfully.”

“It could end up getting done or not,” the official said. “Everybody appears to be trying to get a compromise bill that really works.”

A spokesman for the governor, Kevin Quinn, said the Patakis’ trip does not preclude progress at the negotiating table. “Wherever he goes, the governor is still governor,” Mr. Quinn said. “Given the modern-day technology that exists in the 21st century, he’s going to keep in touch with his senior staff on a regular basis to monitor what’s going on in Albany.”

Mr. Pataki’s paternal ancestors are Hungarian, and he has visited the country before. The governor’s aides would not specify which countries he would see on this trip. They did say the governor and his family will fly on commercial airlines, stay in hotels, and pay their own expenses. In the past, Mr. Pataki has come under fire for accepting free flights and accommodations from groups and individuals doing business with the state.