These officials said Mr. Obama made his wishes known to Sen. Max Baucus, D-Mont., at a White House meeting attended by administration officials and senior Democratic lawmakers.
It was not immediately clear whether Mr. Obama expressed a preference for a bipartisan measure - which Baucus has been laboring over for months - or a bill tailored more to Democratic specifications.
The conversation underscored Mr. Obama's determination to push legislation through both houses of Congress before lawmakers go home for a summer break late this month or in August.
The officials who spoke did so on condition of anonymity, saying they were not authorized to discuss private meetings.
Scott Mulhauser, a spokesman for Baucus, said the senior Democrat "has stressed the Finance Committee will be ready when it has a mark (proposal) that can ensure quality, affordable care for every American, lower costs - and pass the Senate."
Despite objections from conservative and moderate Democrats, prospects for House action along the president's timetable are better than in the Senate.
There, majority Democrats are readying legislation, to be introduced as early as Tuesday, that would prohibit insurance companies from denying coverage or charging higher premiums on the basis of pre-existing medical conditions.
The measure would spend billions of dollars subsidizing lower income individuals and families who cannot afford coverage, in an attempt to cut dramatically into the ranks of the uninsured.
To comply with another presidential priority, it would rely on cuts in Medicare and Medicaid to begin slowing the rate of growth in health care spending overall.
The measure is expected to impose a fee equal to 8 percent of a worker's salary on large companies that fail to offer insurance or do not subsidize it at a high enough rate.
Individuals also would have to pay a penalty if they refused to purchase affordable insurance.
Officials announced last week that the measure would include an income tax surcharge on the wealthy, estimated to raise more than $500 billion over the next decade.
Earlier Monday, Mr. Obama delivered a full-throated promise to get comprehensive legislation.
"Don't bet against us. We are going to make this thing happen," he told a news conference intended to focus on his nominee for surgeon general, Dr. Regina Benjamin.
The appearance in the Rose Garden was the president's first public outing since his weeklong overseas trip - and the first after an up-and-down week in Congress.
While the president was out of the country sizing up foreign leaders, rank-and-file lawmakers took a look at the emerging details of health care legislation and many decided they didn't like what they saw. They called a time out. In the House, conservative Democrats rebelled over costs. In the Senate, the Democratic leadership pulled the plug on a controversial financing scheme that a moderate Democrat worked out with Republican counterparts.
Mr. Obama lost no time signaling that he intends to be in the forefront of the action.
"I just want to put everybody on notice, because there was a lot of chatter during the week that I was gone," the president said. "Inaction is not an option."
He also ruled out any tax increase affecting the middle class, complicating lawmakers' efforts to pay for overhaul.
"During the campaign I promised health care reform that would control costs, expand coverage and ensure choice and I promised that Americans making $250,000 a year or less would not pay more in taxes. These are promises that we're keeping as reform moves forward," Mr. Obama said.