Russia said NATO units will not be allowed to go through the former countries of the Soviet Union.
Officials insist only Commonwealth of Independent States (CIS) forces will be allowed to carry out anti-terrorist missions from central Asian states bordering Afghanistan.
But the former head of the Russian Federal Security Service says officers are ready to open their files to US colleagues.
The official Itar-Tass news agency has reported the Russian Defence Minister Mr Sergei Ivanov said NATO cannot operate from within the CIS.
"There are absolutely no grounds, even hypothetical, for suppositions on a possibility of any NATO military operations in the Central Asian states, forming the CIS," he is reported as saying.
Deputy to the State Duma Mr Nikolai Kovalev made the information-sharing offer: "We have a common enemy, and all secret services should help one another for the earliest exposure of the terrorist acts in the United States".
But he said: "When executors and masterminds of the terrorist acts in the US are exposed, Washington should not take an independent decision on wiping out terrorists. "A common decision should be taken by all countries with the participation of the UN Security Council".
PA