"All we're asking for here is a discussion and fairness for the American people over Obamacare," Boehner said, "and I would hope my Democrat colleagues in the Senate would listen to the American people and sit down and have a serious discussion about resolving these differences."
But the Democrats' Senate Majority Leader Harry Reid said, "We're locked in tight on Obamacare."
Earlier Obama had insisted that he would not negotiate until Republican leaders faced down "a faction of the Republican Party that are [sic] willing to burn the house down because of an obsession over my health care initiative".
After the talks the White House issued a statement saying that Obama remains hopeful that "common sense will prevail" in the budget standoff.
"The President made clear to the leaders that he is not going to negotiate over the need for Congress to act to reopen the government or to raise the debt limit to pay the bills Congress has already incurred," the White House said.
The shutdown has seen swathes of the US government closed and 800,000 workers put on unpaid leave, amid warnings from the military and intelligence community that the shutdown is causing serious damage to US security.
Obama's meeting with John Boehner, the Republican speaker of the House, was the first time he has seen his chief opponent since a September 3 meeting about Syria.
Mitch McConnell, the Republican Senate leader, also attended yesterday's meeting along with the President's Democrat allies.
As the political gridlock continued in Washington, Obama cancelled stops in Malaysia and the Philippines during his trip to Asia next week, telling the countries' leaders that his travel was limited by the crisis. James Clapper, the director of national intelligence, said the shutdown was an "insidious" threat to national security that would increase the longer employees were not working.
"This affects our global capability to support the military, to support diplomacy and foreign policy matters," he told the US Senate judiciary committee.
Nearly a million public workers spent a second day on unpaid leave, parks remained closed and cancer patients were turned away from the government's National Institutes of Health (NIH).
Republicans were moving ahead yesterday with a number of "piecemeal" funding bills that would reopen high-profile closures.
Democrats rejected the approach, saying the only solution was a complete reopening of the government.
"They took hostages by shutting down the government and now they're releasing one hostage at a time," said Nancy Pelosi, the Democrat leader in the House.
The White House said it would veto the bills, saying they were not "a serious or responsible way to run the US government".
Boehner accused Mr Obama of a "scorched-earth policy of refusing to negotiate in a bipartisan way" on budget issues or health care.
- Additional reporting, AP
