"What's important is if you are running for president is that the American people know who you are and what you've done and that you're an open book," Obama told WMUR-TV of Manchester, N.H., in an interview on Monday.
"And that's been true of every presidential candidate dating all the way back to Mitt Romney's father," Obama added.
Obama's campaign has also released a new video on Romney's finances.
George Romney, then the governor of Michigan, released 12 years of tax returns when he sought the presidency in 1968.
Mitt Romney has released only his most recent tax returns; Obama's camp is demanding more as they raise questions about Romney's overseas accounts, and whether he has used them to avoid paying U.S. taxes.
Romney and aides also say Obama is attacking him in order to divert voters' attention from a poor economy.
"With the failures of his presidency becoming more evident by the day, Barack Obama has resorted to the tactics of a typical politician," said Romney spokesman Ryan Williams. "Rather than talk about the issues important to Americans in their everyday lives, he has chosen instead to run a campaign based on character attacks and dishonesty."
