US Secretary of State John Kerry was in Moscow on Thursday to see if President Vladimir Putin can be convinced to support an end to Bashar al-Assad's rule in Syria.

Kerry met his counterpart Foreign Minister Sergei Lavrov and was later to head to the Kremlin for talks with the Russian leader and sound him out on the crises in Syria and Ukraine.

The top US diplomat said this week's bomb attacks in Brussels demonstrated that countries must come together to conquer the extremist threat wherever it may strike.

‘I know that many people are very hopeful, Sergei,’ Kerry said, in brief remarks before the two men held closed-door talks at a foreign ministry conference centre in Moscow.

‘Our counterparts, whom you and I have both talked to in the last days, are hopeful that these meetings here in Moscow today have an ability to be able to further define and chart the road ahead so that we can bring this conflict in Syria to a close as fast as possible.’

Lavrov told Kerry diplomatic efforts had been focused on creating a ‘balance of interests’ among all sides involved in the Syrian crisis, including Moscow and Washington.

But US officials fear the Syrian opposition will drop out of UN-mediated peace talks in Geneva unless Russia's ally Assad agrees to step down as part of a political transition.

Putin has stood by Assad, and even sent Russian warplanes to fight to protect his regime and strike the extremist Islamic State group, which has seized territory in the east of the country.

But Moscow recently announced a partial withdrawal of its forces from Syria, creating what Washington believes is an opportunity to press for a change of stance on the regime.

‘What we're looking for, and what we've been looking for, for a long time is how are we going to transition away from Assad's leadership,’ a senior US official told reporters.

- Middle East powerbroker -

In a sign of Russia's strengthened role as a Middle East powerbroker, both Kerry and Putin met separately with the Crown Prince of Abu Dhabi, Mohammed bin Zayed al-Nahyan.

Kerry's visit also comes while Europe faces a security crisis after Tuesday's attacks in Brussels, which left 31 dead and 300 injured.

On Wednesday, Lavrov called for Europe to drop its ‘geopolitical games’ and unite behind efforts to fight terrorism, as Russia continues its air strikes in Syria.

Kerry acknowledged that the ceasefire negotiated by Russia and the United States between Assad and the armed opposition has led to a ‘beneficial reduction’ of violence in Syria.

But he stressed much work lay ahead to secure peace.

‘We both know that more needs to be done in terms of both the reduction of violence and the flow of humanitarian goods,’ Kerry told Lavrov.

After his Moscow visit, Kerry will travel to Brussels to offer Washington's support for Belgium and Europe's efforts to counter violent extremism.