Virginia Gov. Robert F. McDonnell was named chairman of the Republican Governors Association on Monday, giving him a greater platform to raise funds, network and garner national attention should he choose to run for higher office.

The new role will generate more attention for McDonnell, who has been mentioned as a possible vice presidential candidate. He said he intends to complete his term as governor but that he would be willing to serve on a 2012 presidential ticket if asked.

“I’m not campaigning for it. I’m not lobbying for it. I’m not asking for it. I’m not expecting it all,’’ McDonnell said during an interview in Richmond. “All I’ve said is, if any governor in America gets a call from a candidate [who] says, ‘Hey, I’d like you to help my ticket. Would you be on it?’ I’d say, sure, I’d think about it.”

McDonnell’s new post, which he is expected to hold through 2012, pits him against Maryland Gov. Martin O’Malley, a rising star in Democratic circles who serves as chairman of the Democratic Governors Association.

Their success will be tied not only to state budgets and legislative sessions but to the wins and losses in gubernatorial races across the nation. Four states — West Virginia, Kentucky, Louisiana and Mississippi — hold elections in November. Eleven states have elections in 2012.

During his tenure, O’Malley has sought to toughen up the association, using sharper rhetoric than his predecessors. He is critical of GOP gubernatorial candidates and regularly takes aim at what he calls “a new group of tea-partying, FDR-hating Republican governors.”

McDonnell said he plans to promote policies that have worked in Virginia — where the Senate is controlled by Democrats and the House is led by Republicans — and showcase examples of successes from the 29 Republican governors across the country.

“I see my style being the same that it has been for 20 years in office — being a spokesman for the conservative principles I hold dear,’’ said McDonnell, whose gubernatorial term runs through January 2014. “I’m going to be talking about problem-solving and examples of leadership, but I probably am not going to be much of an attack dog.”

The dominance of Democrats in Maryland has given O’Malley considerably more latitude than some of his association predecessors in making the case against Republicans. He has singled out several GOP governors during appearances around the country but has steered clear of deriding McDonnell. In fact, in February, when O’Malley delivered his first keynote speech as chairman to a Democratic dinner in Virginia, his most pointed criticism was of New Jersey Gov. Chris Christie (R).

McDonnell said that he and O’Malley get along well — working together on everything from Metro and criminal-justice issues to the Chesapeake Bay — and he doesn’t expect that to change, although he said the two disagree on taxes, regulation and unions.

O’Malley aides also say the governors have forged a productive relationship. Although Maryland and Virginia compete for jobs, their markets are affected by many of the same regional issues, including federal government employment and contracting, so the two governors share some policy interests.

While sparring between the heads of the governors associations is inevitable, O’Malley aides suggested that the animosity should be less visible with McDonnell at the helm.

“This has never been about attacking the chair of the other committee,” said Democratic association spokeswoman Elisabeth Smith. “Whether the RGA chair is [Texas Gov.] Rick Perry or Bob McDonnell, Governor O’Malley will continue to focus on winning races in 2011 and 2012.”

McDonnell, Virginia’s first Republican governor in eight years, took office in 2010 after the biggest economic crisis since the Great Depression. He easily defeated his Democratic opponent, state Sen. R. Creigh Deeds (Bath), by running as a pragmatic leader who could work across party lines to solve the state’s economic problems.

A Washington Post poll in May showed that 62 percent of Virginians approved of the way McDonnell was handling his job, while 26 percent disapproved.

McDonnell has appeared on network television, most notably following last year’s response to President Obama’s State of the Union address. And the governors association post would mean more meetings with national donors, regular appearances on Sunday morning talk shows and a more direct voice in the national political dialogue.

On Friday, GOP officials announced that McDonnell will headline a fundraiser next month in New Hampshire — his first trip as governor to the state that hosts the first-in-the-nation presidential primary.

McDonnell was appointed chairman after Perry, who had been serving as the group’s leader, entered the presidential race over the weekend.

Virginia Democrats immediately criticized McDonnell for taking the post, even though former Gov. Timothy M. Kaine served as chairman of the Democratic National Committee and former Democratic governor Mark R. Warner, now a U.S. senator, served as chairman of the nonpartisan National Governors Association.

“As Virginians cope with the loss of 14,000 jobs in the month of June, it’s clear that he’s hoping [presidential hopefuls] Michele Bachmann or Rick Perry will whisk him away before the bill comes due for his failed agenda,” said Brian Coy, a spokesman for the Democratic Party of Virginia.

McDonnell was one of many who criticized Kaine for serving as DNC chairman his final year as governor because they said he spent too much time away from Virginia.

“The problem with the DNC chair is [that it’s] a full-time job,’’ he said. “It’s a full-time, paid job that governor Kaine was trying to do part time while he was part-time governor, and that was my criticism. I think this is very different.”

Republicans have openly criticized O’Malley — and some Democrats grumble more privately — about the time the governors association post takes from Annapolis. O’Malley has bristled at the charge, pointing out that his travels usually do not take him out of state overnight.

Since he became chairman of the governors association in December, O’Malley’s national political profile has risen considerably, with invitations to speak at Democratic dinners around the country and on television talk shows.