The first UK foreign secretary in Tehran since 1979
Mr Straw - the first UK foreign secretary to visit Tehran since the 1979 Islamic revolution - is seeking Iranian support for the US-led international campaign against terrorism.
But Dr Kharrazi warned against "rash, hasty action" that would lead to insoluble problems.
Mr Straw's visit to Tehran has infuriated Israelis after comments published in an Iranian newspaper in which he said that anger over events "in Palestine" helped breed terrorism.
Israeli Prime Minister Ariel Sharon has decided not to meet Mr Straw when he flies to Israel later on Tuesday.
The term "Palestine" implies an element of statehood which Israel does not recognise.
Britain says "no offence was intended" in the remarks.
Political minefield
Mr Straw's visit to Tehran comes as the Western powers are making a concerted effort to persuade Muslim governments that the coalition against terrorism is directed at fanatics - not at Islam.
He told the Iranian foreign minister that the UK "would share what [evidence] we could, confidentially. But I don't think anyone is in much serious doubt about the guilt of Osama Bin Laden".
Iran, Mr Straw said, "is an important source of advice on Afghanistan". But he said the UK was not seeking military help from Iran in any US-led strikes against the Taleban, which has sheltered Bin Laden since 1996.
Iran - which has more than two million Afghan refugees - and the Taleban have extremely hostile relations.
Tehran is fearful that US-led action against the Taleban could lead to a further influx of refugees, even though it has attempted to seal its border with Afghanistan.
Those fears were reflected in Mr Kharrazi's comments: "A rash, hasty action will lead in the long run to insoluble problems. We must avoid ways that cause catastrophe," he told reporters.
He said an international consensus for strikes against the Taleban would have to include public opinion in the region.
The BBC Tehran correspondent says the implication seems to be that Iran would not object to a surgical move to get rid of the Taleban quickly and cleanly.
Mr Straw later met President Mohammad Khatami, who has led efforts to liberalise Iran.
UN campaign
Our correspondent says that, despite their differences, the country's hardliners and reformers agree that Iran will not simply join an American-led coalition against the Taleban.
President Khatami himself has recently tried to promote the idea of international action against terrorism through a campaign pursued under the auspices of the United Nations.
The UK broke off diplomatic relations with Iran in 1989, after the late Ayatollah Khomeini called for the death of the British author Salman Rushdie for allegedly insulting Islam in his writing.
But ambassadors were exchanged again after 10 years.
Mr Straw said he was not carrying any message from the United States.
The Americans, who do not have diplomatic ties with Tehran, have welcomed Iran's condemnation of the attacks on New York and Washington.