Her comments came as the Foreign Secretary, Jack Straw, repeated the Government's concerns that Iran is behind attacks on British soldiers in Iraq.
Downing Street said Mr Blair and Ms Rice discussed the need for Iran to meet its "international obligations".
Britain believes that the insurgents targeting its troops in southern Iraq are being trained by an elite arm of Iran's armed forces. Defence sources say the explosives that have killed eight British soldiers had been supplied by Hizbollah via the Iranian Revolutionary Guard.
In an interview with the BBC, Ms Rice called on Iran to become "good neighbours" with Iraq. "I trust the British on this issue because the British are operating in the south. They know the situation there," she said.
The constitutional referendum in Iraq yesterday was an "important milestone", she said, and the insurgents attempting to wreck the creation of a permanent government would fail.
"The insurgency can't ultimately survive without a political base," she said. "Even though there are a few violent men who can always wreak havoc, who can always grab the headlines, who can always kill innocent men, women and schoolchildren, the Iraqi political process goes on and the Iraqis are taking advantage of it."
The talks with Mr Blair at Chequers was the last leg of Ms Rice's European tour to press for a diplomatic solution to the Iranian nuclear issue. She is believed to have discussed how the US and Britain hope to prevent the country from developing nuclear weapons, which it denies wanting to do.
Mr Straw underlined suspicions that Iran had a hand in bomb attacks on British troops in Iraq. "What we have presented to the Iranians is evidence which, in our judgement, clearly links the improvised explosive devices which have been used against British and other troops, mainly in the south of Iraq, to Hizbollah and to Iran."
Iran's ambassador to Britain, Dr Seyed Mohammad Hossein Adeli, told BBC Radio 4's The World This Weekend: "We have already rejected categorically any link between Iran and the incidents that have taken place in Iraq for the British troops. There is not any kind of direct or indirect connection with Iran."Reuse content