On the recession, he said: "America and a few countries cannot be expected to bear the burden of the fiscal and interest rate stimulus alone. We must share it globally.
"So let us work together for the worldwide reduction of interest rates and a scale of stimulus round the world equal to the depth of the recession and the dimensions of the recovery we must make."
Mr Brown added: "An economic hurricane has swept the world, creating a crisis of credit and of confidence.
"History has brought us now to a point where change is essential. We are summoned not just to manage our times but to transform them."
In addressing Congress, Mr Brown follows in the footsteps of Winston Churchill, Clement Attlee, Margaret Thatcher and Tony Blair.
He said: "Now more than ever the rest of the world wants to work with you...
"And let me say that you now have the most pro-American European leadership in living memory. A leadership that wants to cooperate more closely together, in order to cooperate more closely with you.
"There is no old Europe, no new Europe. There is only your friend Europe.
Gordon Brown seemed to offer a lot of warm words but very few hard plans to fight the recession
Vince Cable, Lib Dems
"So once again I say we should seize the moment - because never before have I seen a world willing to come together so much. Never before has that been more needed."
Announcing the honorary knighthood for Edward Kennedy, Mr Brown said that "Northern Ireland is today at peace, more Americans have healthcare, more children around the world are going to school" because of the long-serving Democratic senator.
The world owed "a great debt to [his] life and courage", he added.
Senator Kennedy, who is being treated for a brain tumour, was unable to attend Congress.
BBC political editor Nick Robinson said US President Barack Obama had telephoned Mr Brown during his flight back to the UK to congratulate him on his speech.
But he said the US administration had "only just begun to engage with the ideas that are coming from Gordon Brown, let alone agree to them".
Conservative Party acting leader William Hague said: "It is right [of Mr Brown] to remind Americans that we need to work together against protectionism, in defeating terrorism and in combating climate change.
"What was missing was any sense of contrition for past mistakes and an ability to translate words into action."
Liberal Democrat Treasury spokesman Vince Cable said: "Gordon Brown seemed to offer a lot of warm words but very few hard plans to fight the recession which has engulfed the world economy and his government.
"Rather than trying to shore up his reputation in America, he should be focusing his attention on fixing the mess we face back home."
After Mr Brown's meeting with Mr Obama on Tuesday, the US president said the "special relationship" between the countries would "only grow stronger".
After about an hour of talks at the White House, Mr Brown and Mr Obama said they agreed that improvements were needed to the regulation of the global banking system.
Mr Obama warned that countries should not "project inwards" by encouraging protectionism during the economic crisis.
Mr Brown said the two countries were pursuing a "common interest" in a "global new deal".
The prime minister's US visit comes ahead of a summit of the Group of 20 (G20) developed and emerging economies in London on 2 April.
The EU and Canada have warned that a "buy American" clause in the US economic recovery package could promote protectionism.
It seeks to ensure that only US iron, steel and manufactured goods are used in construction work funded by the bill - but has included a pledge to respect international trade obligations.
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