The Browns greet President Barack and Michelle Obama at No 10
Barack Obama has praised Gordon Brown's "integrity" as the two men vowed to work together to tackle the "unprecedented" global recession.
Speaking after two hours of talks, the US president said there was "enormous consensus" on tackling the crisis.
And he rejected talk of splits ahead of the G20 summit of world leaders.
The official business of the G20 began later with a working dinner in Downing Street, ahead of the conference proper in London's Docklands on Thursday.
At the dinner, Mr Brown sat between the presidents of China and Indonesia while President Obama sat next to German Chancellor Angela Merkel and the president of South Korea.
Earlier, Mr Brown and President Obama appeared relaxed as they faced reporters in Downing Street, with Mr Brown praising Mr Obama's presidency as giving "renewed hope" to the world.
Mr Obama hailed the "special relationship" between Britain and the US and the "kinship" he felt with Great Britain.
Both men played down reports of a rift between different countries on the best way to rescue the world economy.
Mr Brown said: "President Obama and I are agreed about the significance of this week's G20 meeting that the world is coming together to act in the face of unprecedented global financial times."
He rejected reports French President Nicholas Sarkozy was ready to walk out of Thursday's summit, telling reporters in Downing Street: "We are within a few hours of agreeing a global plan for economic recovery and reform."
G20 LONDON SUMMIT
World leaders are meeting this week in London to discuss measures to tackle the downturn. See
our in-depth guide
to the G20 summit.
The G20 countries are Argentina, Australia, Brazil, Canada, China, France, Germany, India, Indonesia, Italy, Japan, Mexico, Russia, Saudi Arabia, South Africa, South Korea, Turkey, the UK, the US and the EU.
Mr Obama said there had been "great symmetry" between the US and UK in their discussions on the best way to deal with the economic crisis.
"I am absolutely confident that the United States as a peer of these other countries will help to lead us through these very difficult times."
Asked what advice he had for Mr Brown about winning elections, Mr Obama said that whatever the problems faced, "good policy" would win out "over time".
He told Mr Brown to continue showing "integrity" and to be sure that "every day you are waking up and making the very best decisions that you can despite the fact that sometimes the cards in your hand are not very good and the options are narrow".
But he stopped short of wishing the England football team good luck in its World Cup qualifier against Ukraine, saying: "The last thing I'm going to do is wade into European football. That would be a mistake. I didn't get a briefing on that, but I think that would be a mistake."
The president later met Tory leader David Cameron at the US Ambassador's residence.
Mr Cameron earlier welcomed the Obamas' visit to Britain at prime ministers' questions in the Commons, but pressed Mr Brown to use the G20 summit to persuade America to restart the Doha world trade round.
He also accused the prime minister of failing to lead by example on Britain's public finances.
"Once the talks are over, Britain will still be left with the most appalling public debt," he told Mr Brown, adding: "We should never leave Britain this exposed again."
Lib Dem leader Nick Clegg welcomed G20 discussions on tax havens but said the prime minister had presided over "industrial scale tax avoidance in British banks and British businesses".
Mr Brown said the G20 were on the "verge of an agreement" that would mean that every country would have to give information on their tax haven status.
Mr Brown later held talks at No 10 with Russian President Dmitry Medvedev, Chinese president Hu Jintao, Indian prime minister Manmohan Singh and Japanese counterpart Taro Aso.
World leaders are gathering in London to discuss ways to resolve the worst financial crisis since the 1930s, with the summit taking place amid tight security.
About 5,000 demonstrators gathered in the City of London during the day and 26 were arrested during scuffles with police.
Some protesters got on to the roof of the Bank of England, while windows were broken at a nearby branch of RBS.
The two-day summit officially began on Wednesday evening as the leaders from the G20, which groups the world's most powerful economies, attended a working dinner at No 10.
The G20 summit will be crucial for Gordon Brown, whose reputation for economic competence has been battered by the financial crisis.
He has sought to lead the drive for a global approach to the crisis and the meeting is an opportunity to restore his image as a competent economic manager.
President Obama and the first lady later held a private meeting with the Queen at Buckingham Palace.
Labour donor JK Rowling was among the Browns' dinner guests
Before the meeting, the president said he was really looking forward to the occasion, saying the Queen's "decency and civility" were important to people across the US.
Mr Obama and wife Michelle were earlier greeted in Downing Street by Gordon Brown and wife Sarah.
Mrs Brown hosted a dinner for the G20 spouses at 11 Downing Street at the same time and with the same menu as the leaders' banquet next door at No 10.
Mrs Obama was seated between Harry Potter author JK Rowling and Olympic gold medallist Dame Kelly Holmes.
Rowling is a longstanding Labour supporter who donated £1m to the party last year while Olympic gold medallist Dame Kelly was one of London's ambassadors in the successful bid to host the 2012 Olympics.
Other guests included supermodel Naomi Campbell, Martha Lane Fox, founder of the website lastminute.com and a trustee of legal action charity Reprieve, Paralympian Dame Tanni Grey-Thompson, Bend It Like Beckham film director Gurinder Chadha, Gavin and Stacey actress actress Ruth Jones, psychologist Tanya Byron and broadcaster Emma Freud.
The menu was prepared by celebrity chef Jamie Oliver and featured seasonal produce including Welsh lamb, Jersey Royal new potatoes and asparagus.