The two leaders were also set to discuss ways to tighten global financial controls, a key issue at the G20 summit of developed and emerging economies that Brown will host in London on April 2.
Brown is the first European leader to meet Obama since he took office on January 20.
The UK prime minister is also set to address US politicians at a special session of the US congress on Wednesday.
Brown, a former finance minister who has faced plummeting opinion poll ratings in the UK, is also hoping for a political boost from his meeting with Obama, whose approval ratings in the US remain high just six weeks into his administration.
The high profile accorded to Brown's visit has not ended worry in the UK about whether the relationship between the two nations would remain as "special" as ever.
"Our relationship is terrific," Obama said, praising Brown for his efforts to grapple with the struggling UK economy.
However, a joint press conference set to be held on Tuesday was cancelled in what UK media reports described as a possible snub to the British prime minister.
UK officials reportedly said the press conference was cancelled because of heavy snow on the White House grounds.
Brown's call for a "global New Deal" paid tribute to the policies of Franklin Roosevelt's New Deal that lifted the US out of the Great Depression of the 1930's.
The meeting came amid continuing turmoil on the global markets.
On Monday, US stocks fell to their lowest levels in more than 11 years after US insurance giant AIG reported a $61.7bn loss, the worst ever for a US firm.
"A lot of people looking at this downturn are looking also at the way we can create a better and stronger and more stable economy in the upturn," Brown told US National Public Radio (NPR) earlier on Tuesday.
"What you really need is a better early warning system. What you need are better rules and standards that can be adopted and can be understood to be the fair ones across the system. What, of course, you need is governments that are prepared to take the supervisory action."