The Obama re-election campaign has accepted at least one foreign donation in violation of the law — and does nothing to check on the provenance of millions of dollars in other contributions, a watchdog group alleges.

Chris Walker, a British citizen who lives outside London, told The Post he was able to make two $5 donations to President Obama’s campaign this month through its Web site while a similar attempt to give Mitt Romney cash was rejected. It is illegal to knowingly solicit or accept money from foreign citizens.

Walker said he used his actual street address in England but entered Arkansas as his state with the Schenectady, NY, ZIP code of 12345.

“When I did Romney’s, the payment got rejected on the grounds that the address on the card did not match the address that I entered,” he said. “Romney’s Web site wanted the code from the back of card. Barack Obama’s didn’t.”

In September, Obama’s campaign took in more than $2 million from donors who provided no ZIP code or incomplete ZIP codes, according to data posted on the Federal Election Commission Web site.

The Obama campaign said the FEC data was the result of “a minor technical error.”

“All the ZIP codes and numbers are real and can be verified,” spokesman Michael Czin said.

The Obama campaign’s apparent lack of safeguards makes it possible to violate the law, says a report released by the Government Accountability Institute, a Florida-based watchdog group.

The report found that one Obama site — Obama.com — gets almost half of its traffic from foreign computer addresses. The site directs users to an Obama donation page.

“We are not suggesting that just foreign traffic by itself is a problem,” said Peter Schweizer, president of the GAI. “But for a campaign that is very sophisticated in its fund-raising capabilities, they do not make one effort to try to even see or ask somebody to check a box that says they are a US citizen.”

Obama’s re-election campaign took in $130,867 from donors who provided no ZIP codes and $2 million from those with incomplete ZIPs in September.

That same month, Romney’s campaign recorded $2,450 from donors without ZIP codes and $2,500 from those with incomplete ZIPs.

Walker said it should have been clear to the Obama campaign’s computers that his donations came from a computer with a foreign IP address.

The Obama campaign says it “screens all credit-card contributions that originate from a foreign IP address” and requests proof of citizenship if questions arise.

But not only did Walker’s Obama donations go through, but he said he began receiving two to three e-mail solicitations a day to give more. The e-mails asked for $188 or more.

If Walker gave $188, his total contribution to Obama would be $198 — less than the $200 threshold at which campaigns have to identify the donor to the FEC.

“I have not had any e-mails asking for proof of identity,” Walker said.

The GAI report found the Obama campaign Web sites do not ask donors to provide their three-digit card-verification value, or CVV, numbers to ensure they are the legitimate holders of the card. Romney’s campaign asks for such information, which is considered a standard security measure.

One conduit for Obama donations is Obama.com, which was registered in 2008 to Robert Roche, an American who lives and works in China, where he owns an infomercial company.

Roche is also a bundler for the Obama campaign and was given a seat at the head table for a 2011 state dinner with the Chinese president

The GAI report said that the site registration was changed in 2010 to make it anonymous and that it was unclear whether Roche still owns it.

Roche’s mother in Chicago referred calls to the Obama campaign. The campaign declined to comment.