By Ginger Gibson

WASHINGTON (Reuters) - U.S. Republican Donald Trump said on Tuesday his "unlimited" trove of personal wealth would help compensate for his poor presidential campaign fundraising, even as he took steps to court new donors to help win the White House.

The New York real estate mogul raised only $3.1 million in individual contributions in May and ended the month with $1.3 million in cash, leaving him far behind his Democratic rival Hillary Clinton who brought in $26 million and closed the month's books with a $42 million war chest.

The figures underscore the huge cash advantage Clinton is hoping to enjoy leading into the Nov. 8 presidential election, one that could allow her a large staff and millions of dollars of television and digital ads in battleground states.

Trump, who openly shunned donations while winning the party nomination, rebuffed criticism from Republicans who say he needs to raise cash for the general election fight against Clinton. His campaign might need in excess of $1 billion by some estimates but Trump said money was not a problem.

“If need be, there could be unlimited 'cash on hand' as I would put up my own money," Trump said in a statement, which asserted he had already spent over $50 million dollars on his bid for the White House.

The billionaire candidate added that his campaign also costs less than a traditional one because it is "is leaner and more efficient, like our government should be."

Trump has said he is worth more than $10 billion, but much of his money is tied up in properties and businesses. Estimates from outside groups have put Trump's wealth as low as $1 billion. Forbes magazine estimates it at $4.5 billion.

According to Trump’s most recent personal financial disclosure with the Federal Election Commission, in May, he had between $65 mln and $175 million in liquid assets – money in funds, equities and cash.

Despite Trump's professed lack of concern for standard campaign fundraising, he took steps to boost donations.

Several sources with knowledge of Trump’s fundraising activities said he will attend a dinner on Tuesday evening to court hedge fund managers and other Wall Street donors.

Woody Johnson, the billionaire investor and owner of the New York Jets football team, is also hosting a breakfast for Trump at a high-end restaurant in Manhattan on Wednesday morning.

Targeting smaller donors, Trump on Tuesday also sent his first email asking for donations, telling supporters that he will match their contributions up to $2 million.

Trump's allies, donors, and other Republican operatives have expressed concerns about his campaign operation, which has been dogged by internal battles, a threadbare campaign infrastructure, and thin fundraising apparatus.

"Without money you don’t have a campaign," said Stan Hubbard, a Republican donor from Minnesota who owns a chain of radio stations and who has contributed to Trump.

"He’s got to call on people to give money and stop all this nonsense about funding his own campaign," Hubbard said.

Trump this week fired his campaign manager, Corey Lewandowski, who had been overseeing the campaign's fundraising arm.

UNUSUAL CANDIDATE

Trump has spent much of the race so far breaking the mold of a traditional campaign, defeating a crowded field of primary opponents who vastly outspent him in ads and staff.

During the Republican primary race, he often told his supporters not to contribute money and ridiculed opponents for accepting cash from special interest groups and wealthy contributors.

He has so far showed little interest in calling donors to ask for money for his general election battle. He only began holding in-person fundraisers in late May.

"Trump defeated the most talented GOP field in a generation with less staff, less experience and less money in much less time," said Republican strategist Keith Appell.

"That said, Trump’s campaign needs to transition quickly to a national, general election effort online, on the air and on the ground – his populist, anti-Washington, new leadership message has been muddled by sideshow issues."

Trump has loaned his campaign $46 million since launching last year, federal filings show. He often uses his own plane to travel to campaign events, and also uses his hotels and other properties as venues - expenses he is required by law to reimburse from his campaign funds.

The campaign has spent about $6.2 million with Trump businesses including TAG Air and his Mar-a-Lago property in Florida. It has also reimbursed Trump about $390,000 for some payroll and other expenses.

The Republican National Committee, meanwhile, announced it raised $11 million in May, and had $19.9 million in cash at the beginning of June. The RNC will help Trump's effort to get elected, but also helps fund congressional races.

(Additional reporting by Grant Smith, Michelle Conlin, Emily Flitter, Olivia Oran and Lawrence Delevingne in New York, Eric Walsh in Washington; Editing by Bill Trott and Alistair Bell)