Russia's military chief said the US had its own weapons
But Russia's Chief of Staff, General Anatoly Kvashnin, on Friday said any military participation is unlikely while Defence Minister Sergei Ivanov rejected suggestions Nato forces might launch attacks on Afghanistan from former Soviet republics.
"The United States has armed forces powerful enough to handle the task by themselves," General Kvashnin said.
Republics ruled out
He said there had been no consultations at a military level between the two countries on retaliatory attacks.
It has been suggested that the former Soviet republics which border Afghanistan might be the base for any US strike against the Saudi-born dissident Osama Bin Laden.
Mr Bin Laden - the chief suspect behind Tuesday's attacks - is believed to be hiding in Afghanistan.
But this idea was quashed Mr Ivanov.
"I don't see any basis for even the hypothetical possibility of Nato military operations on the territory of Central Asian nations that belong to the Commonwealth of Independent States," he told reporters.
He announced a meeting of CIS defence ministers for 26 September.
Foreign Minister Igor Ivanov, who had previously pledged to support all means necessary to deal with terrorism, also struck a more cautious note, saying retaliatory attacks would not provide a long-term solution.
"What we need is long-term co-operation and steps aimed at preventing such tragedies," he said in an interview with CNN.
Conflicting interests
Moscow has its own interests in tracking down Mr Bin Laden and might be able to provide the US with essential information about his movements.
Not only did he fight against the Soviet Union in the 1980s, but he is also accused of bankrolling the Islamic fighters waging war on Russian troops in Chechnya.
But analysts say Russia may fear that attacks by the United States could extend to what the US considers "rogue states" such as Iran, which are allies of Russia.
And any attack on Afghanistan could provoke a flood of refugees, destabilising the already fragile Central Asian states.