Relations between the alliance and Moscow were frozen after Russia's brief war with Georgia in August.
US Secretary of State Condoleezza Rice said she broadly backed efforts to improve relations but that some areas remained "problematic".
The ministers are also expected to discuss an increase in Nato co-operation with Georgia and Ukraine.
The meeting is not expected to resume the Nato-Russian Council, say analysts, but could lead to a resumption of lower-level dialogue with Moscow.
BBC diplomatic correspondent Jonathan Marcus says the alliance seems polarised with one camp, including the United States and many of newer European members, eager to draw Georgia and Ukraine ever closer to Nato.
Countries like Germany, France and Italy though are much more cautious. They are worried about worsening tensions with Moscow, BBC correspondent says.
Ms Rice said she was not opposed "in principle" to improving the council's activities, but warned against military cooperation.
"We should be very attentive to what the Russians are doing and are they living up to their obligations," she said.
"There are certain types of activities, like military-to-military contacts, that seem to me to be problematic, when the Russian ministry is sitting in Georgian territory, in the separatist regions."
Thousands of Russian troops are still stationed in the territories of South Ossetia and Abkhazia.
Caution
The leaders are also expected to encourage Georgia and Ukraine to pursue the reforms needed to join Nato - a bid opposed by Russia.
However, the ministers are expected to stop short of proposing formal steps towards full Nato membership.
The Georgian conflict in the summer raised doubts among some members, including Germany and France, that it was not yet ready to join the alliance and remained too volatile.
Ms Rice said she believed in Nato's "open door policy" but that there should be "no shortcuts to membership of Nato" and both Ukraine and Georgia must first meet the organisation's admission standards.
"No one wants to see a circumstance in which Ukraine and Georgia are shut out," she said.
BBC
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