Click here to see a map of bases the US might use
US Secretary of State Colin Powell said anything which could weaken the Taleban would be helpful.
In a further boost to American diplomacy, Saudi Arabia announced on Tuesday that it was breaking off relations with the Taleban, in a
statement released by the official SPA news agency.
The United Arab Emirates broke off relations three days ago.
This leaves Pakistan as the only country that still recognises the regime in Afghanistan.
More arms
President Putin has further increased the pressure on the Taleban by saying that Russia would offer more arms and other supplies to the Northern Alliance, the group fighting the Taleban in northern Afghanistan.
For its part, the US administration has moved to cut off the flow of money to Osama Bin Laden, his al-Qaeda network and other groups it suspects of involvement in terrorism.
President Bush announced he had signed an executive order freezing the US assets of 27 individuals and organisations, as the country prepares for military action in response to the suicide attacks on New York and Washington.
In other developments:
- Afghanistan's ruling Taleban movement admits it has lost ground to opposition forces in heavy fighting in the north of the country
- Taleban supreme leader Mullah Mohammed Omar says Washington cannot resolve the current crisis by killing either himself or Bin Laden
- Share prices in the US and Europe post strong gains, recovering some of last week's hefty losses
- UK Foreign Secretary Jack Straw arrives in Iran, seeking Tehran's support for the anti-terrorism campaign
- A high-level European Union delegation is due to hold talks with the Pakistani government on Tuesday, at the start of a regional tour of Asia and the Middle East
- The World Health Organisation urges governments to prepare for possible chemical airborne raids
Russia's offer
The BBC's correspondent in Moscow, Caroline Wyatt, says Mr Putin's most important offer to the US was to allow it and its allies to use former Soviet airbases in the countries surrounding Afghanistan.
Mr Putin said that those states, including Uzbekistan, Tajikistan and Turkmenistan, shared Russia's position.
And Russia will offer further pooling of intelligence, the president said, prior to leaving on a visit to Germany on Tuesday.
Before outlining his plan, Mr Putin held marathon meetings with his top security, defence and intelligence chiefs and met with leading parliament members.
One liberal parliament member was quoted by the Reuters news agency as saying that the president has ruled out sending troops into Afghanistan, where the Soviet Union had lost 15,000 soldiers in the 1980s.
Mr Putin also spoke on the phone to the presidents of the five central Asian nations, and met with a group of Russia's Islamic leaders.
Opening shot
In Washington, Mr Bush described his executive order as a "strike on the financial foundation of the global terror network," saying this was the opening shot of a war against terrorism that would be waged on several fronts.
"Money is the life-blood of terrorist operations," the president said during a news conference in the White House Rose Garden. "Today, we're asking the world to stop payment."
US Attorney General John Ashcroft has meanwhile confirmed that one of the suspects recently arrested in connection to the attacks on New York and Washington had sought data on using a crop-dusting plane.
This has raised concern that militants have also been planning an airborne chemical attack in the US.
As part of the heightened state of security in the US, federal aviation officials said they were considering banning carry-on baggage and early seat selection.
Two-thirds of the major cities in the US are planning to revise their emergency procedures in the light of the 11 September attacks, according to a report published on Monday.
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