The White House has said the president believes he should pay more tax as the release of Barack Obama's returns showed he was taxed at a higher rate than his Republican presidential rival, Mitt Romney, last year but below many ordinary Americans.

The president's joint tax return with his wife, Michelle, released by the White House on Friday, reveals they paid tax at a rate of 20.5% on income of $789,674 in 2011.

The Obamas' earnings fell by nearly $1m on the previous year as sales of the president's bestselling books declined. The first couple paid $162,074 in income tax. They also donated a similar amount to 39 charities.

The vice-president, Joe Biden, and his wife, Jill, paid tax at 23% on income of $379,035.

The release of the returns was politically charged because the president has built part of his re-election campaign around accusing the Republicans of giving millionaires tax breaks paid for by cutting services to the less well off.

The White House has also targeted Romney, who paid tax at less than 15% over the past two years on his multimillion-dollar income from a vast fortune.

Obama has been campaigning for the imposition of the "Buffett rule" that would see those earning more than $1m a year, whether from salary or investments, pay tax at a rate of at least 30%. The rule is named after the business magnate, Warren Buffet, who called for the rich to pay more to the treasury because he said it is wrong that he should be taxed at a lower rate than his secretary.

The White House acknowledged that the president believes he should pay more tax.

"Under the president's own tax proposals, including the expiration of the high-income tax cuts and limitations on the value of tax preferences for high-income households, he would pay more in taxes while ensuring we cut taxes for the middle class and those trying to get in it," it said.

The president's tax policy is aimed at the Republicans in general and directly at Romney, his likely rival in the presidential election, who has an estimated fortune of $220m yet paid tax at a rate of less than 15% on income of $45m over the past two years. Most of the income, which places Romney in the top 1% of earners in the US, was derived from investments, which are subject to a lower tax rate.

Romney has refused to release his tax returns for before 2010.

Obama's campaign manager, Jim Messina, on Friday used the release of the president's returns to accuse Romney of continuing to hide his own declarations from the time he made most of his fortune.

"Governor Romney has yet to provide tax returns from the period in which he made hundreds of millions as a corporate buyout specialist, or as governor of Massachusetts, the experience he says qualifies him to be president," he said.