Mr Obama reminded his opponents that his approach to avoiding steep tax hikes and spending cuts due in January, which could trigger another recession, had just won the backing of Americans at the polls.
He spoke just hours after John Boehner, the Republican Speaker of the House of Representatives, repeated his party's commitment not to raise anyone's tax rates as part of a deal to address the fiscal crisis.
In his first event at the White House since beating Republican Mitt Romney in Tuesday's election, Mr Obama called on Congress to work with him to produce a plan and invited congressional leaders to meet with him next week.
He said: "I'm not wedded to every detail of my plan. I'm open to compromise. I'm open to new ideas."
The "fiscal cliff" of steep government spending cuts and tax increases, which are due to be brought in under existing law in early 2013, is Mr Obama's most pressing challenge after winning a second term. Aimed at cutting the federal budget deficit, the planned measures are due to take an estimated $600 billion out of the economy and severely hinder economic growth.
Mr Obama said voters supported his ideas, including raising taxes on the wealthiest Americans.
He said: "I just want to point out, this was a central question during the election. It was debated over and over again. And on Tuesday night we found out that the majority of Americans agree with my approach."
Earlier, Mr Boehner called on the president to play a more active role in addressing the issue and urged the president to take the lead in negotiations.
The Republican said: "This is an opportunity for the president to lead. This is his moment to engage the Congress and work towards a solution that can pass both chambers."
While disagreeing on immediate measures to avert the crisis, Mr Obama and Republicans may find common ground on more far-reaching measures to reduce the deficit, including an overhaul of US tax law.
The non-partisan Congressional Budget Office repeated its stance on Thursday that, if left unaddressed, the abrupt fiscal tightening would knock the economy back into recession, with unemployment rates potentially soaring back to about 9%. The rate is now 7.9%.
However, it also warned of serious trouble ahead if the United States does not stem the growth of its exploding deficit.
Separately, a poll of economists carried out by Reuters found that the majority believe partisan squabbling over the budget crisis will harm the US economy.
Meanwhile, a video of a tearful Mr Obama following his victory has been released by his campaign team. An emotional Mr Obama tells staff members he is proud of the work they did, then pauses to wipe away tears.