Romney's success will depend, at least in part, on his ability to compete financially with Obama.
The Republican's campaign had about $10 million in the bank at the end of March, according to federal filings. Obama reported having more than $104 million in his account; he'd already spent $90 million on the general election.
Romney was eager to turn the political page after Tuesday's primary wins in New York, Pennsylvania, Connecticut, Rhode Island and Delaware.
"After 43 primaries and caucuses, many long days and not a few long nights, I can say with confidence — and gratitude — that you have given me a great honor and solemn responsibility," he told supporters gathered in New Hampshire. He urged all who are struggling in a shaky economy to "hold on a little longer — a better America begins tonight."
Romney is only 300 delegates away from the 1,144 delegates it takes to formally secure his party's nomination, and that could happen by the end of May.
Obama set the modern fundraising record in 2008, when he and his Republican rival, Sen. John McCain, spent more than $1 billion combined; Obama spent more than $730 million.
The two major-party candidates set a spending record of $700 million in 2004.
Obama opened his finance events to press coverage in June 2008 after he became the presumptive Democratic nominee and largely plays by the same rules as president. Reporters are allowed in if he makes remarks during the event, regardless of size, and are kept out if there are no formal remarks.
Romney's campaign has refused to provide specific times and locations of this week's fundraisers.
Associated Press writers Kasie Hunt and Jim Kuhnhenn contributed to this report.
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