Obama deputy campaign manager Stephanie Cutter said in a statement the disclosure "continues to mask Romney's true wealth" and income from the private equity firm he once led, leaving the American people in the dark about critical details of his finances.
Senate Majority Leader Harry Reid, D-Nevada, called the new tax information insufficient.
"What we don't know is why he refuses to be straight with the American people about the choices he's made in his financial life," according to a statement from Reid, who previously created a stir when he alleged Romney paid no taxes in some years but refused to divulge the source of his accusation.
"When will the American people see the returns he filed before he was running for president?" Reid asked.
Obama responds to health care attacks
In his appearance by satellite at the AARP event in New Orleans, Obama responded to specific attacks on the health care law by Ryan and other Republicans, declaring the 2010 measure cuts waste and fraud in Medicare, provides preventive care to keep people healthier and reduces prescription drug costs for seniors.
Savings come from "using the purchasing power of Medicare to say to doctors and hospitals and insurance companies: 'You guys need to work smarter,'" Obama said to applause. "Instead of having five different tests that each of you is charging for, do one test and email it to everybody."
Ryan, the conservative House Budget Committee chairman from Wisconsin, has proposed a partial privatization of the entitlement that would provide government subsidies to help senior citizens pay for coverage they would choose from a list of options.
He defended the plan Friday in the face of a mixed reception.
"The first step to a stronger Medicare is to repeal Obamacare because it represents the worst of both worlds," Ryan said to loud booing. He added: "I had a feeling there'd be mixed reaction so let me get into it ."