WASHINGTON — Vice President Dick Cheney said Tuesday he supports President Bush’s call for a federal constitutional amendment banning same-sex marriages, though one of his daughters is gay and he has said in the past the issue should be left to the states.

“The president’s taken the clear position that he supports a constitutional amendment,” Cheney said in an interview with MSNBC. “I support him.”

Cheney said during the 2000 campaign, and again last month, that he prefers to see states handle the issue of gay marriage. His openly lesbian daughter, Mary Cheney, is an aide in the Bush-Cheney re-election campaign, but the vice president declined to discuss her.

“One of the most unpleasant aspects of this business is the extent of which private lives are intruded upon when these kinds of issues come up,” he said. “I really have always considered my private — my daughters’ lives private and I think that’s the way it ought to remain.”

Cheney said he will be on Bush’s re-election ticket in the fall, as the president himself has said, although there is speculation to the contrary. Cheney, who has had four heart attacks, said his health has been good and he couldn’t think of any circumstances that would prompt to decline the role.

“He’s asked me to serve again and I’ll be happy to do that,” Cheney said.

He dismissed talk that he has become a liability to Bush, with Democrats pounding the administration over allegations of profiteering in Iraq by oil services giant Halliburton, which Cheney once headed, and the vice president’s frequent but now much-doubted claims that Iraq had weapons of mass destruction.

“I think the fact that you become a lightning rod is, it goes with the turn,” he said. “I’m not concerned about that.”

Cheney’s popularity with the public has dropped in recent weeks, according to the National Annenberg Election Survey. In October, 43 percent of the public had a favorable view and 26 percent had an unfavorable view. In the last two weeks of February, people were about evenly split, with 33 percent favorable and 36 percent unfavorable.

The vice president’s popularity declined with most groups, with the biggest drop among Republicans. Seventy-four percent of Republicans saw him favorably in October and 58 percent viewed him that way in late February. Six in 10 in late February said Bush should keep Cheney as his running mate, while a quarter said Bush should pick someone else.

The Annenberg survey in late February of 2,700 people has a margin of sampling error of plus or minus 2 percentage points

In his interview, the vice president also took a shot at the leading Democratic presidential candidate, Sen. John Kerry of Massachusetts, and his chief rival, Sen. John Edwards of North Carolina, who have skewered Bush over lagging job growth even as the economy improves.

“If the Democratic policies had been pursued over the last two or three years, the kind of tax increases that both Kerry and Edwards have talked about, we would not have had the kind of job growth that we’ve had,” Cheney said.