UK Prime Minister Tony Blair has told the Iraqi president British troops will stay in the country "as long as he wants them".
The visit is Mr Talabani's first European trip since coming to power
Speaking after talks in London, Jalal Talabani said an early withdrawal of US and UK troops would be a "catastrophe".
Mr Blair issued a warning to Iran not to interfere in Iraq following claims it was supplying weapons to insurgents.
He said devices which killed British troops looked like those used by Iran but stressed "we cannot be sure".
Both leaders reiterated that British forces were in Iraq under a United Nations mandate with the support of the Iraqi government.
Mr Blair said: "There is no justification for Iran or any other country interfering in Iraq."
He said Britain would not "be subject to any intimidation".
Mr Blair's comments came just days after a senior British official had accused Iran's Revolutionary Guard of supplying the lethal explosive technology responsible for killing British soldiers in Iraq.
The Iranian government in Tehran denounced the claim as a lie.
Mr Talabani, on his first visit to Europe since taking office in April, thanked Britain for liberating Iraq from the "brutal dictatorship" of Saddam Hussein.
He said: "With the help of our allies the people of Iraq are now free. They are enjoying all kinds of democratic rights.
"Iraqis are building a democracy on the ruin of a country shattered by brutal dictators."
He described Iraq under Saddam Hussein as "a concentration camp above ground and a mass grave beneath it", saying the Iraqis would always be grateful for their liberation.
The talks came ahead of next week's crucial referendum on a new Iraqi constitution, which will be followed by elections.