Mitt Romney’s presidential campaign shot past President Obama’s in fund-raising in May, collecting more than $76.8 million, nearly $17 million more than his Democratic rival.

The Republican success suggests that Mr. Romney is the beneficiary of the usual cash rush from donors who are eager to back the presumptive nominee now that the party has united behind him. The amount raised for Mr. Romney and his party was nearly double what they collected the prior month, and it was disclosed just hours after Mr. Obama’s campaign announced Thursday that its joint fund-raising operation with the Democratic National Committee had raised $60 million.

The fund-raising announcements came on a day of dueling speeches from Mr. Romney and Mr. Obama.

Campaigning in St. Louis, Mr. Romney accused the president of not believing in or understanding America’s free enterprise system.

“There is something fundamentally wrong when there are over 23 million Americans who are unemployed, underemployed, or have stopped looking for work, and yet the president tells us he’s doing a great job,” Mr. Romney said. “I will not be that president of deception and doubt.”