NATO and Russian military brass went into talks Wednesday, bound in outrage over terrorism after Moscow's airport bombing, but at odds over cooperation on a missile shield for Europe.

Russian General Nikolai Makarov flew into Brussels to meet with fellow chiefs of staff from the 28-nation alliance in the latest step in thawing ties between the former Cold War foes following Russia's 2008 war with Georgia.

The NATO-Russia Council, the forum for discussion between the two military powers, issued a statement condemning Monday's "terrorist bombing" at Domodedovo airport.

"Our countries stand together in the fight against terrorism, and we are determined to expedite our efforts to counter this scourge," the statement said.

NATO chief Anders Fogh Rasmussen, who has championed better ties, had already offered the Western alliance's "solidarity" after the death of 35 people in the suicide attack.

"We are in this fight together," he said after Monday's blast. "This is why in the NATO-Russia Council we have to strengthen our cooperation in the fight against terrorism."

Wednesday's talks follow a landmark Lisbon summit in November, when Russia agreed to allow NATO to transport more goods to Afghanistan through its territory, and explore the possibility of working with the Western alliance on the missile defence system.

NATO decided at Lisbon to deploy radars and missile interceptors to protect Europe from rogue attacks, and invited Moscow to cooperate in the project to ease Russian fears that the system was aimed against its nuclear deterrent.

But the military powers have since then offered differing visions about the shield, with NATO insisting on keeping two independent systems and Russia calling for a "sectoral" system, in which each side would shoot down missiles coming from a certain geographic area.

"We don't really get what the Russians really want," a NATO official told AFP. "I find it surprising they think we want one system. It's too big a jump."

Russian President Dmitry Medvedev this week called on NATO to provide a clear answer over his country's role in the European missile shield, warning that Moscow could deploy more nuclear weapons if it was left out of the umbrella.

"Our partners have to understand that we do not want this simply to have some common toys that NATO and we can play with, but because we want adequate protection for Russia," Medvedev said in televised remarks on Monday.

"So this is not a joking matter. We expect from our NATO partners a direct and unambiguous answer," said Medvedev, who has demanded an equal role for Russia in the US-European missile project.

Rasmussen, in a video blog last week, said the two systems should remain separate but could cooperate by sharing information and developing "potential synergies".

"The vision of the alliance is for two independent but coordinated systems working back to back," Rasmussen said.

The meeting of Russian and NATO military chiefs came the same day that Russia gave final approval to a nuclear disarmament treaty with the United States, a major step in Washington's own "reset" of relations with Moscow.

"I also hope that political momentum generated by this treaty will help Allies and Russia to make concrete progress in their strategic partnership, including in the field of missile defence," Rasmussen said.