US hawks take a tough line against Iraq
He was speaking after the Iraqi Deputy Prime Minister, Tariq Aziz, said he believed the US planned to attack 300 Iraqi targets with 1,000 missiles.
The US blames the suicide attacks on Saudi-born dissident Osama Bin Laden who is believed to run his al-Qaeda network from Afghanistan.
Mr Rumsfeld, also interviewed by ABC, said: "There is no question but that Iraq is a state that has committed terrorist acts and has sponsored terrorist acts."
He said that Iraqi President Saddam Hussein was a threat to other countries including the US and that many people - in and out of government - wished he were not there, adding: "And certainly, I'm one of them."
Terror links required
Last Wednesday, US Secretary of State Colin Powell and Jack Straw said Iraq could become a target if evidence was found linking it to specific acts of terrorism.
Asked if the US planned to target the Iraqi leader in the next phase of its war on terror, Mr Rumsfeld said that President George Bush had said the fight was against all terrorist networks.
"There are many more than just al-Qaeda," he said.
"They are in many more countries beyond Afghanistan. It is something that we as a country and the many countries assisting us are currently doing."
He was also asked about the significance of a meeting in Prague earlier this year between a suspected pilot of one of the hijacked planes that crashed into New York's World Trade Center on 11 September and an Iraqi intelligence agent.
Mr Rumsfeld replied: "We will know that only after the proper law enforcement people investigate that. Clearly, the meeting is not nothing, it is something notable."
Threat to coalition
In a rare interview with a western newspaper, Mr Aziz told the Sunday Telegraph that an attack on Iraq would inflame Arab opinion and cause the US-led coalition to fall apart.
He said Britain might also be involved, but that Iraq was ready to defend itself.
Mr Aziz said the war on terrorism would only be a pretext, since Iraq had nothing to do with the events of 11 September or the anthrax attacks in the US.
What Washington really wanted, he said, was to crush an independent nation that will not bow to Western pressure.
Mr Aziz did not predict any military intervention by Arab states on Iraq's side.
But he said indignation in the Arab world would destroy the US-led coalition.
According to Mr Aziz, Iraq rebuilt its armed forces during the 1990s, but it does not retain any stocks of anthrax.
BBC correspondent Stephen Cviic says there is no doubt some US officials would like to make Iraq a target in the war on terrorism. Their main objective would be to depose President Saddam Hussein.
Clear evidence needed
But this view is not unanimously held either in Washington or London, and there is no immediate sign of military action spreading beyond Afghanistan.
Mr Straw said: "I can tell you that Iraq has not been targeted."
He added: "You only take military action where there is the clearest possible evidence of culpability and where military action is the
only option left," he said.
Hundreds of European firms are expected to take part in the Baghdad international trade fair which opens on Thursday.
Organisers expect it to be the biggest turnout since a UN embargo was imposed on Iraq 11 years ago.
Iraq has been under UN sanctions since invading Kuwait in 1990, but an "oil-for-food" arrangement allows it to sell oil under UN supervision to meet humanitarian needs.