It comes after Nato member Turkey said Russian jets had violated its airspace.
Russia has fired missiles from a warship in addition to air strikes to support Syrian leader Bashar al-Assad.
But Moscow denies Western accusations that its strikes have mainly hit Assad opponents, some supported by the West, and not Islamic State (IS) militants.
BBC defence correspondent Jonathan Marcus says Nato aims to make clear it will respond to any challenge.
Russia wants to show that Western policy in Syria has failed and there are other forces to be supported there, primarily President Bashar al-Assad.
The Kremlin’s desire appears to be aimed at keeping America on the back foot.
The use of cruise missiles on Wednesday does not change the situation militarily – the same effect could have been achieved by air strikes.
But Mr Putin wants to project his power on the world stage, to show that he is a force to be reckoned with.
On Thursday, Nato Secretary-General Jens Stoltenberg said the alliance had expressed its concern over Russia’s “strong and increased military presence” in Syria.
He called on Moscow to play a “constructive and co-operative role” to fight IS and to stop supporting Mr Assad.
But he added that the situation underlined the need for political initiatives to end Syria’s war.
UK Defence Secretary Michael Fallon is expected to announce that Britain is ready to make a long-term troop deployment to the Baltic republics, our correspondent says.
But, he adds, ministers are meeting amid a deepening sense of crisis.
On Wednesday, Russia said it had launched missile strikes against IS from warships in the Caspian Sea – about 1,500km (930 miles) away.
Russia’s foreign ministry also said Moscow was willing to establish contact with the Free Syrian Army – a Western-backed rebel group – to discuss fighting IS “and other terrorist groups”.
But US Defence Secretary Ash Carter said coalition forces fighting IS in Syria would not co-operate with Russia.
“We believe Russia has the wrong strategy,” he said. “They continue to hit targets that are not IS.”
Russia’s air campaign in Syria has raised fears of accidental contact between Russian warplanes and those of the US-led coalition which have been targeting IS for the past year.
Pentagon officials revealed they recently had to carry out at least one “safe separation” manoeuvre to avoid a US jet coming too close to a Russian aircraft over Syria.
Russia’s envoy to Ankara was summoned three times in response to recent incursions into Turkey’s airspace.
Turkish President Recep Tayyip Erdogan warned the Kremlin that any “attack on Turkey means an attack on Nato”.
“If Russia loses a friend like Turkey, with whom it has a lot of co-operation, it is going to lose a lot of things. It needs to know this,” Mr Erdogan said.
The Syrian civil war began with an uprising against President Assad in 2011 that was brutally put down. It has since deteriorated into fighting between pro-government forces and various rebel groups – some of which also fight each other.
Amid the chaos, IS militants have seized swathes of territory in Syria and Iraq.