US Secretary of State John Kerry said Thursday he and Russian President Vladimir Putin had agreed to push the Syrian regime and rebels to accelerate talks on a political transition to end their civil war.

Kerry would not say whether Putin had agreed that Syria's President Bashar al-Assad should step down as part of the transition but insisted that Russia and the US agreed the strongman "should do the right thing" and engage in the peace talks.

"We agreed on a target schedule for establishing a framework for a political transition and also a draft constitution, both of which we targeted by August," Kerry said at a joint news conference with Foreign Minister Sergei Lavrov after meeting with Putin at the Kremlin for over four hours. 

Lavrov told journalists that Moscow and Washington would now step up efforts to get the Syrian regime and opposition to hold "direct talks" in Geneva, where a round of negotiations that saw a United Nations mediator shuttle between the delegations concluded on Thursday. 

"As the immediate task we have agreed to push for the soonest start of direct talks between the government delegation and the whole spectrum of the opposition" that will help move toward "a transitional governance structure" in the war-torn country, Lavrov said.

Kerry jetted in to Moscow to sound out Putin over whether his stance has softened on ally Assad's future after Russia announced on March 14 that it was withdrawing the bulk of the forces it had sent to prop up his troops.  

Kerry said the two sides were looking to bolster a month-old ceasefire between Assad's forces and the opposition hammered out by Putin and US President Barack Obama that has seen fighting drop.  

"We agreed today to build on recent gains to take immediate steps to reinforce the cessation of hostilities," Kerry said, adding this included "steps to end the use of any indiscriminate weapons, to halt attempts by either side to seize new territory and to finalise a common understanding for how this cessation can be institutionalised."

"We agreed that the regime and the opposition need to begin releasing detainees," he added. 

Ties between Russia and the US are at their lowest point since the Cold War over the Kremlin's meddling in Ukraine and Kerry insisted Washington was not backing down on the crisis. 

Kerry said Ukraine's territory still includes the Crimean peninsula, which Russia annexed two years ago, as well as disputed rebel-held areas in the east of the country.

He also said that he had raised the issue of freeing Ukrainian pilot Nadiya Savchenko after she was sentenced this week to 22 years in jail over the killing of two Russian journalists following what the West has condemned as a politically motivated sham trial.