* Pro-Obama Super PAC raised $4 mln in May
* Pro-Romney PAC raised $5 mln, American Crossroads $4.6 mln
* Democrats chasing after Republicans in Super PAC money race
By Alina Selyukh and Alexander Cohen
WASHINGTON, June 20 (Reuters) - The outside "Super PAC" helping U.S. President Barack Obama's re-election campaign raised $8 million in May and so far in June, marking its best months ever as it tries to catch up to deep-pocketed Republican rivals in the money chase ahead of the Nov. 6 election.
In federal filings released on Wednesday, Priorities USA Action reported raising $4 million in May and having $4.5 million left in cash on hand. A source familiar with the group's fundraising said Priorities has brought in another $4 million this month.
The Super PAC backing presumed Republican nominee Mitt Romney raised $5 million in May and had $8.2 million left in cash on hand, according to its report filed with the Federal Election Commission.
Democrats had badly struggled to narrow the Super PAC fundraising gap, caused in part by Obama's own early cash advantage and the party's distain for unrestrained fundraising and spending allowed for such groups.
The 2012 election is on track to become the most expensive in U.S. history and outside spending has already topped $100 million.
Since Romney effectively clinched his party's nomination in mid-April, his campaign has been closing in on Obama, leaving Democratic operatives fretting he will become the first incumbent to be outspent in the race.
In May, for the first time, Romney's campaign fundraising - donations subject to legal limits - topped Obama's, bringing in more than $76.8 million. Obama and his Democratic allies raised some $60 million in the same period.
Wednesday's filings showed Obama and the Democratic National Committee had $139.4 million left on hand at the end of May.
Romney's campaign said together with its party allies it had $107 million left in cash on hand. Only $77.8 million of that has been reported, with the rest presumably sitting in the joint fund shared by Romney and the Republican National Committee that is due to report for the first time next month.
An Obama campaign official on Wednesday laid the ground for a chance that Romney would keep outraising Obama, predicting the Republican would raise $100 million in June and through the year, he and various Republican outside groups would spend $1.225 billion on TV advertising.
American Crossroads, a Super PAC run by former George W. Bush aide Karl Rove, is another well-heeled group helping Romney bridge the cash gap with Obama.
In May, it raised $4.6 million and had $29.4 million in cash left to spend. Crossroads has a non-profit sister group, Crossroads GPS, that is not required to disclose donors.
In May, Crossroads GPS matched a $25 million TV advertising blitz announced by the Obama campaign, helping Romney keep cash in reserve. The two groups have said they plan to spend upward of $300 million this election season.
Priorities has so far spent some $15 million on advertising, much of it in recent weeks on ads across six states hitting Romney on his private equity past and immigration positions.
The pro-Obama group plans to spend another $10 million on the air through the end of summer, the spokesperson said.
Restore Our Future on Wednesday launched a $7.6 million ad spree in nine battleground states, picking on Obama's gaffe earlier this month that "the private sector is doing fine."
Much of Restore Our Future's cash in May came from first-time donors, including a $500,000 check from Arkansas billionaire investment banker Warren Stephens.
Another check of that size came from Pennsylvania healthcare executive and founder of Select Medical Rocco Ortenzio, whose total donation is now $750,000.
Three companies linked to Robert Brockman, an executive at Dayton, Ohio-based Reynolds and Reynolds, split $1 million in donations. The companies - CRC Information Systems Inc, Fairbanks Properties LLC and Waterbury Properties LLC - share a P.O. box with Brockman's car dealership support company.
Notably absent from the filing is billionaire Las Vegas casino magnate Sheldon Adelson, whose $10 million pledge to the group this month is expected to be disclosed in July.
Adelson jumped into the spotlight after he and his family sent $21.5 million to a Super PAC backing a now-failed Republican presidential bid by Newt Gingrich. The Super PAC in May reimbursed Adelson's wife Miriam for $5 million of that.
Crossroads received a $1 million donation from Dallas-based real estate investment firm Crow Holdings, for a total of $1.5 million in contributions from the company. Billionaire coal executive Joe Craft of Tulsa, Oklahoma gave $1.25 million in addition to his company's total gift of $850,000.
Priorities received three $1 million checks in May from Houston lawyer Steve Mostyn and Florida retiree Barbara Stiefel, as well as Franklin Haney, CEO of Washington-based real estate firm FLH Company.