Clinton also urged Nato members to help Ukraine and Georgia find ways to join the alliance.
"We should continue to open Nato's door to European countries such as Georgia and Ukraine and help them meet Nato standards," she said.
Russia strongly opposes alliance membership for the two former Soviet states because Moscow fears Nato is expanding into its sphere of influence.
The agenda of the talks in Brussels will also include the success of Nato's faltering mission in Afghanistan.
Barack Obama, the US president, is looking to re-start co-operation with Russia via the joint Nato-Russia Council.
"It is important that Nato moves to re-establish the Nato-Russia Council," David Miliband, the British foreign minister, said before the meeting.
"Russia needs the West as much as the West needs to re-engage with Russia," he said.
"We have obvious common interest with Russia: Afghanistan, counter-terrorism, the fight against proliferation of weapons of mass destruction and others," Jaap de Hoop Scheffer, Nato secretary general, said.
"We are not shying away at all from the serious differences of opinion that remain between Nato and Russia, in particular about Georgia," de Hoop Scheffer said.
It is believed that the foreign ministers will agree to resuming high-level talks with Russia and assert Georgia and Ukraine's continued inclusion in the organisation.
Official high-level Nato-Russian talks were suspended after Moscow's war with Georgia, however an informal dialogue took place in December.