But he said if it ignored UN resolutions, they would intensify sanctions and face "further isolation".
President Bush said Tehran's demand for nuclear power for civilian purposes was "justifiable" - but could be met by Russia's offer to supply them with fuel.
In a message to Tehran, he said: "You bet you have a sovereign right, absolutely, but you don't have the trust of those of us who have watched you carefully when it comes to enriching uranium."
Mr Brown said Britain would urge Europe to impose "further sanctions" on Iran and Europe would take action to freeze the overseas assets of the country's biggest bank and impose new sanctions on oil and gas.
President Bush thanked Mr Brown for his "strong statement" and added: "The Iranians must understand that when we come together and speak with one voice we are serious."
Let me thank President Bush for being a true friend of Britain
He said pressure was necessary to "solve this problem diplomatically" - but added: "Iranians must understand, however, that all options are on the table."
Mr Brown, who became prime minister a year ago, and President Bush, who leaves office in six months' time, also discussed Afghanistan, with Mr Brown announcing there would be an increase in British troop numbers.
Mr Brown described the US president as a "true friend of Britain" while President Bush praised Mr Brown for being "tough on terror" and said it was in "all our interests" to help people in Afghanistan and Iraq.
And he dismissed reports of a split between the UK and US on troop numbers in Iraq as "typical".
"He's left more troops in Iraq than initially anticipated and like me, we will be making our decisions based on conditions on the ground... without an artificial timetable."
President Bush said history would judge whether the military tactics could have been different in Iraq, but he stood by the decision to remove Saddam Hussein as the right one for "our security", for peace and for 25 million Iraqis.
He said it was important to support democracy "at the heart of the Middle East".
"It's a democracy that's not going to look like America, it's not going to look like Great Britain, but it's a democracy that will give government responsive to the people."
He said it had "absolutely" been worth it and democracy in Iraq would make it easier to deal with "the Iranian issue" and would send a message to reformers and dissidents.
He dismissed the idea that "perhaps freedom is not universal - maybe it's only western people who can self govern" as "the ultimate form of political elitism".
After the press conference in Downing Street, Mr Bush and Mr Brown travelled to Stormont, Belfast, for talks with Northern Ireland First Minister Peter Robinson and his deputy, Martin McGuinness.
President Bush spent the day in London and Belfast
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