NATO allies and Russia vowed Thursday to deepen their cooperation but remained deeply at odds over a US-led missile shield in Europe and the situation in Syria.

Despite rifts on several fronts, Russian Foreign Minister Sergei Lavrov and NATO recalled after talks in Brussels that both sides have teamed up to fight terrorism and piracy, and cooperate on Afghanistan.

"It is well known that we do not agree on all issues, but it is also clear that we are committed to continue discussing all issues at all times," NATO Secretary General Anders Fogh Rasmussen said.

But the former Cold War foes have failed to reach a compromise on the missile defence system, which Russia fears would thwart its nuclear deterrent despite NATO assurances that it is aimed at Iran and other threats.

"Our missile defence system is not designed to threaten Russia or undermine the strategic position of Russia," Rasmussen said.

Russia has demanded legally-binding guarantees that the missile shield will not undermine its arsenal, but NATO refuses to enter into such an agreement and has instead offered political reassurances.

"We need clear guarantees that it is not targeted against us," Lavrov told a news conference.

NATO leaders are hoping to declare the start of an "interim capability" for the missile shield at a summit in Chicago on May 20-21.

The alliance had hoped to invite Russia's president-elect Vladimir Putin, but he is unlikely to attend, with NATO officials citing the Russian leader's busy political calendar.

Lavrov met with US Secretary of State Hillary Clinton and her 27 NATO counterparts as violence continued in Syria despite the presence of UN observers.

While Western powers have urged Russia to press the Syrian regime to end the violence, Lavrov countered that the opposition was to blame too and nations with influence on them should pressure them to respect a week-old ceasefire.

"I have today called on my colleagues to abandon the rhetoric of self-fulfilling prophecies that (UN-Arab League envoy) Kofi Annan's plan will certainly fail," he told a news conference.

"Before thinking about what to do in the future, we should do everything to make this plan successful," he said.

After the NATO talks, Clinton, who warned Wednesday that Assad's regime could face extra measures if the UN peace plan fails, was to join 13 other foreign ministers in Paris for talks on Syria.

French Foreign Minister Alain Juppe warned that Russia's refusal to support efforts to put pressure on Assad was plunging Moscow deeper into international isolation on the issue.

"The major responsibility for what is happening in Syria is on the Syrian government. They should ensure the human rights, the security of their citizens and the sovereignty of their state," Lavrov said.

But the Russian minister accused the opposition of trying to undermine the UN observer mission in order to pave the way for the creation of buffer zones or military-backed security corridors.

Russia has met with members of the opposition but lacks the influence that other members of the UN Security Council and Arab nations have on them, he said.

"The crisis cannot be solved if outside players do not demand the same thing from all conflicting parties in Syria: to stop shooting, give observers a possibility to evaluate the situation and shift to political dialogue," he said.

While Russia cooperates with NATO on Afghanistan, allowing the alliance to ship equipment through its territory, Lavrov criticised plans to withdraw combat troops by the end of 2014.

"As long as Afghanistan is not able to ensure by itself the security in the country, the artificial timelines of withdrawal are not correct and they should not be set this way," Lavrov said.