They later said the session was "good" and "useful," providing hope that negotiations on raising the debt ceiling and reopening the federal government might at long last get under way.
Obama met at the White House with about 20 Republican lawmakers from the lower chamber after the Grand Old Party (GOP) (as Republican Party is commonly known as) earlier in the day had presented a plan to raise the debt ceiling for six weeks to allow time for negotiations on the budget.
The debt ceiling must be raised by Oct 17 or else the federal government will not be able to pay its bills and will default for the first time in history.
The president had a "good meeting" with Republican legislators although he issued no comment about the Republican proposal, the White House said in a statement.
The White House hastened to add, however, that no specific agreements were made at the meeting, saying only that Obama and other top administration officials listened to Republican proposals and discussed "potential paths forward."
The president "looks forward to making continued progress" on resolving the impasse so that the US can "pay the bills we've incurred" and the government shutdown can be brought to an end, the statement said.
Republican House Majority Leader Eric Cantor of Virginia told reporters at the Capitol that the meeting was "useful" and both sides agreed to continue talking.
Cantor also said that the two sides would continue talking Thursday evening and expressed the hope that a clearer path forward would emerge.