HARTFORD, Conn - Less than a day into the US general election campaign, probable Republican nominee Mitt Romney stumbled on a key issue on Wednesday in an early warning that he needs to sharpen up quickly to compete with President Barack Obama.

Romney made a disputed claim that the vast majority of US jobs lost under Obama were held by women, and his campaign team struggled to say whether their candidate supports a fair pay law for women.

Romney is now under pressure to show he can take on Obama's well-organized campaign, after main Republican rival Rick Santorum quit the White House race on Tuesday and left the former Massachusetts governor as the presumptive nominee.

In an attempt to deflect Democrats' accusations that Republicans have launched a war on women by criticizing birth control, Romney produced a statistic in a television interview that was questioned by fact checkers.

"Over 92 percent of the jobs lost under this president were lost by women. His policies really have been a war on women," he told Fox News. Romney later repeated the number, which his campaign has used several times in recent days, in a speech in Hartford, Connecticut.

Fact checking website Politifact branded the claim "mostly false." But the Romney camp stuck by the 92 percent figure, which it said was based on women accounting for 683,000 of the 740,000 nonfarm payroll jobs lost from January 2009 to March 2012.

An NBC News fact check quoted a Bureau of Labor Statistics economist as saying of the Romney campaign's claim: "The math they use is correct; the terminology is completely wrong."

The Romney camp missteps were notable in that women voters are a weakness that Romney needs to address ahead of the Nov. 6 election. Obama holds an advantage with women in polls and recent Republican comments on contraception have likely helped widen that gap.

Romney aides ran into trouble on a conference call held with reporters on Wednesday ostensibly to criticize Obama's handling of the economy for women.

A reporter asked if the candidate supported the Lilly Ledbetter Act in favor of fair pay for women, the first law Obama signed and one Republican lawmakers voted against.

"We'll get back to you on that," an unidentified adviser said. The Romney campaign later said he backed the law and released a flood of statements attacking Obama's record on creating jobs for women.

"Of course Mitt Romney supports pay equity for women. The real question is whether President Obama supports jobs for women," said Romney campaign spokeswoman Amanda Henneberg.

Obama has gone on the offensive against Romney in recent days, naming him as a supporter of planned steep budget cuts and portraying him as a millionaire elitist.

LATEST GAFFE

Wednesday was not the first time the Romney team has followed up a campaign victory with a gaffe.

In late March, after Romney won the Illinois primary, adviser Eric Fehrnstrom stepped in hot water by saying that Romney would pivot to the general election like shaking up an "Etch A Sketch."

"The pattern continues - good news followed by self-inflicted wounds the next day," said Juleanna Glover, a Republican strategist and a former adviser to Jon Huntsman's presidential campaign.

"Seems like the campaign is a bit masochistic sometimes, doesn't it? ... It takes time for a presidential (campaign) to compile an all-terrain/all-knowing policy team.

"And it also takes time for the senior staff to be reminded of all the niche issues they've learned and forgotten," she said. 

One Romney official said Wednesday's fuss was the first of many skirmishes the two campaigns will enjoy over the next several months.

"What you're looking at right now is fighting tactic for tactic - all day, everyday - every minute of the news cycle, all the way to November," the official said.

Romney faces a potentially difficult few days. On Thursday, Democrats such as Massachusetts Governor Deval Patrick plan to highlight the sixth anniversary of Romney's Massachusetts healthcare plan that has been criticized by Republicans.

And on Friday, Romney will address the National Rifle Association, or NRA, convention in St. Louis.

Romney came under fire from conservatives during the primary for his past support of gun control measures, criticisms that surrogates from the Obama campaign are likely to discuss on Friday, according to a Democratic official.