The video from the super-PACs features clips of Texas Gov. Rick Perry (R) calling on Romney to provide additional documentation during the GOP primaries.
"It is important for Mitt to release his tax returns. I mean the fact is, we can't fire the nominee in September," Perry says in a Fox News interview shown in the video.
The outside spending groups Priorities USA Action and American Bridge 21st Century echoed the Obama campaign and other Democrats in pressing Romney to release more extensive tax documentation.
“By withholding his tax returns, Mitt Romney is deliberately preventing the American people from fully vetting his candidacy. This is a dangerous precedent leaving the impression he has something to hide and can’t be trusted. Only he can rectify this by immediately by releasing his returns," said Rodell Mollineau, of American Bridge 21st Century, in a statement.
The Obama campaign released a Web video Sunday slamming Romney for alleged reliance on tax havens and renewing calls for greater disclosure.
Romney has released his 2010 tax returns and estimates for 2011, but has declined to unveil further information.
The former Massachusetts governor responded to the criticism in a radio interview tapped Monday, saying there's "nothing hidden" in his tax returns.
"I don't manage them. I don't even know where they are," Romney said. "That trustee follows all U.S. laws. All the taxes are paid, as appropriate. All of them have been reported to the government. There's nothing hidden there."