Donald Rumsfeld, the Defence Secretary, insisted on the United States’s right to a free hand when it came to force in the pursuit of individuals, networks and states implicated in the loss of more than 5,000 lives.

President Bush used a fresh tack to try to persuade Arab states traditionally wary of dealing with America to co-operate. He said they could share information with Washington covertly and their citizens would never know.

However, the White House’s rejection of the need for future UN consent raised concerns that Mr Bush was heading for immediate diplomatic trouble as he tries to piece together a shifting, multilayered pattern of alliances to support a global battle with terrorism lasting years.

China has said that it believes firm evidence should be laid before the UN before any military action. Russia has yet to show its hand on the issue, but US diplomats fear that Moscow will demand thorough discussion at the UN Security Council, where it holds a veto.

In another day of hectic diplomatic activity, Mr Bush met Megawati Sukarnoputri, President of Indonesia, the most populous Muslim country. Sitting side by side, he extended a new offer to leaders in Arab states, saying he would respect their local sensitivities in dealing with the US.

Although some moderate Middle Eastern countries such as Saudi Arabia have sympathised with the US after last week’s attacks, none has agreed to co-operate fully.

Mr Bush said he understood that some countries would be nervous of being seen to deal with their traditional foe. “I understand that,” he said, adding that they could share information in private.

The President said: “This will be a different kind of battle, a series of battles. They will be fought visibly sometimes, and sometimes we’ll never see what may be taking place.

“We fully understand that some nations will be comfortable supporting overt activities, some nations will be comfortable supporting covert activities, some nations will only be comfortable in providing information. Others will be helpful and only feel comfortable helping on financial matters.”

Washington widened its list of possible culprits yesterday, saying it believed that more than one overseas government may have supported the suicide hijackers.

John Ashcroft, the Attorney General, said it was “pretty clear” that a “variety of foreign governments” were involved in supporting and protecting “the networks that conduct these kind of events”.

Mr Ashcroft, visiting the blackened rubble of the Pentagon, said that those governments should understand that “America will not tolerate that kind of support”.