NEW YORK (Reuters) - Hillary Clinton's family's charities are refiling at least five annual tax returns after a Reuters review found errors in how they reported donations from governments, and said they may audit other Clinton Foundation returns in case of other errors.

The foundation and its list of donors have been under intense scrutiny in recent weeks. Republican critics say the foundation makes Clinton, who is seeking the Democratic presidential nomination in 2016, vulnerable to undue influence. Her campaign team calls these claims "absurd conspiracy theories."

The charities' errors generally take the form of under-reporting or over-reporting, by millions of dollars, donations from foreign governments, or in other instances omitting to break out government donations entirely when reporting revenue, the charities confirmed to Reuters.

The errors, which have not been previously reported, appear on the form 990s that all non-profit organizations must file annually with the Internal Revenue Service to maintain their tax-exempt status. A charity must show copies of the forms to anyone who wants to see them to understand how the charity raises and spends money.

The unsettled numbers on the tax returns are not evidence of wrongdoing but tend to undermine the 990s role as a form of public accountability, experts in charity law and transparency advocates told Reuters.

"If those numbers keep changing - well, actually, we spent this on this, not that on that - it really defeats the purpose," said Bill Allison, a senior fellow at the Sunlight Foundation, a government transparency advocacy group.

For three years in a row beginning in 2010, the Clinton Foundation reported to the IRS that it received zero in funds from foreign and U.S. governments, a dramatic fall-off from the tens of millions of dollars in foreign government contributions reported in preceding years.

Those entries were errors, according to the foundation: several foreign governments continued to give tens of millions of dollars toward the foundation's work on climate change and economic development through this three-year period. Those governments were identified on the foundation's annually updated donor list, along with broad indications of how much each had cumulatively given since they began donating.

FOUNDATION DEFENDS TRANSPARENCY

"We are prioritizing an external review to ensure the accuracy of the 990s from 2010, 2011 and 2012 and expect to refile when the review is completed," Craig Minassian, a foundation spokesman, said in an email.

The decision to review the returns was made last month following inquiries from Reuters, and the foundation has not ruled out extending the review to tax returns extending back 15 or so years.

Minassian declined to comment on why the foundation had not included the necessary break-down of government funding in its 990 forms. He said it was rare to find an organization as transparent as the foundation.

"No charity is required to disclose their donors," he said. "However, we voluntarily disclose our more than 300,000 donors and post our audited financial statements on our website along with the 990s for anyone to see."

Separately, the Clinton Health Access Initiative (CHAI), the foundation's flagship program, is refiling its form 990s for at least two years, 2012 and 2013, CHAI spokeswoman Maura Daley said, describing the incorrect government grant break-outs for those two years as typographical errors.

CHAI, which is best known for providing cheaper drugs for tens of thousands of people with HIV around the world, began filing separate tax returns in 2010, and has previously refiled at least once both its 2010 and 2011 form 990s. For both those years, CHAI said its initial filings had over-reported government grants by more than $100 million.

Some experts in charity law and taxes said it was not remarkable for a charity to refile an erroneous return once in a while, but for a large, global charity to refile three or four years in a row was highly unusual.

"I've never seen amendment activity like that," said Bruce Hopkins, a Kansas City lawyer who has specialized in charity law for more than four decades, referring to the CHAI filings.

Clinton stepped down from the foundation's board of directors this month but her husband, Bill Clinton, and their daughter, Chelsea Clinton, remain directors.

The foundation said last week after Hillary Clinton became a candidate that it would continue to accept funding from foreign governments, but only from six countries that are already supporting ongoing projects. CHAI will also continue to receive foreign government funding, again with additional restrictions.

Nick Merrill, Clinton's spokesman, has declined to answer inquiries about the foundation and CHAI.

(This story has been refiled to remove extraneous word in paragraph 5)

(Additional reporting by David Ingram, editing by Ross Colvin)