Obama told lawmakers 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 after the meeting.
Obama reinforced his view that the House should put the clean government funding bill that has been passed by the Senate up for a vote.
"The House could act today to reopen the government and stop the harm this shutdown is causing to the economy and families across the country," the White House said.
In a TV interview, Obama said he was "exasperated" by the sequence of events that led to shutdown of his government and warned the Wall Street that they should also be concerned with this development.
"I think it's fair to say that during the course of my presidency I have bent over backwards to work with the Republican Party and have purposely kept my rhetoric down.
I think I'm pretty well known for being a calm guy. Sometimes people think I'm too calm. And am I exasperated? Absolutely I'm exasperated, because this is entirely unnecessary," Obama told the CBS news in an interview.
Obama warned that investors should be worried.
"This time's different. I think they should be concerned," Obama said.
"When you have a situation in which a faction is willing potentially to default on US government obligations, then we are in trouble," he said.
House of Representative Speaker John Boehner told reporters that Obama during the meeting reiterated one more time that he will not negotiate.
"We sent four different proposals over to our Democrat colleagues in the Senate. They rejected all of them. We've asked to go to conference, to sit down and try to resolve our differences. They don't want to -- they will not negotiate," he told reporters inside the White House after the meeting with Obama.
The US government closed non-essential operations on Tuesday after Congress failed to strike a deal on spending and budget due to differences over 'Obamacare', the signature healthcare programme of President Obama.
Republicans and Democrats are blaming each other for the impasse.
The shutdown has left nearly 800,000 employees on unpaid leave and closed national parks, tourist sites, government websites, office buildings, and more.
"All we want you to do is open the government," Senate Majority Leader Harry Reid told reporters, blaming the Republicans in the House of Representatives for this unprecedented event in nearly 18 years.