Russia on Wednesday said two of its warships were heading back to join its forces in the Mediterranean as President Vladimir Putin opened the new parliament session by calling for a boost of Russia's defences to keep the nation "strong".

"We need to strengthen the security and defence capability of our country to assert its position on the international stage," Putin told deputies.

The decision to send more warships comes a day after Moscow said it had dispatched its S-300 air defence missile system to its naval facility at Tartus in Syria, amid an upsurge in tensions with Washington.

The two Buyan-class corvettes – the smallest class of warship - returned to the Mediterranean after an earlier deployment off the coast of Syria that saw them carry out missile strikes on targets in the war-ravaged country on 19 August.

A spokesman for Russia's Black Sea Fleet told Russian news agencies that the ships left their home port in Crimea on Tuesday as part of a "planned rotation" of Moscow's naval forces in the region.

Russia said last month that it will also send its only aircraft carrier to the region as it looks to bolster support for its bombing campaign in Syria.

The latest moves come as talks on reviving a failed ceasefire were suspended by Washington over Moscow's support of the government in Damascus.

Russia is currently facing the longest economic crisis of Putin's 16-year rule as the Ukraine conflict and a year-old bombing campaign in Syria have pushed tensions with the West to their highest levels since the Cold War.

Putin addressed the State Duma after a crushing victory for ruling party United Russia at elections last month that could help smooth the way for him to claim a fourth term as president in a vote set for 2018.

His speech was mostly focused on the need to keep Russia "strong."

"We must all unite, coordinate our efforts, obligations and rights to maintain Russia's historical supreme right - to be strong," Putin said.

Acrimony between Russia and the United States has surged in recent days after Washington suspended talks on a ceasefire in Syria over Moscow's continuing bombing campaign in support of President Bashar al-Assad.

Moscow has been accused of indiscriminately bombing Aleppo's opposition-controlled east as it helps an offensive currently being conducted by Syrian government forces to capture all of the country's second city.

As a sign of the worsening relations the Duma is looking quickly to ratify two recent decisions by Putin: halting a deal with the US to dispose of weapons-grade plutonium and giving further legal backing to Russia's deployment in Syria.

After delivering his speech, Putin headed to the country's foreign intelligence agency to introduce its newly-appointed boss, former Duma speaker Sergei Naryshkin.

Putin called on the body to resort to "non-standard, unconventional decisions" to cope with threats to the country, Russian news agencies reported.