Pro-government forces pushed a fierce bid to recapture Syria's ancient city of Palmyra from jihadists on Thursday as Moscow hosted top US diplomat John Kerry for talks on the fraught peace process.

The Islamic State group called on civilians still living in Palmyra to leave, as army and pro-government militia battled the jihadists on several fronts along the city's western ring, the Syrian Observatory for Human Rights reported.

IS overran Palmyra - known as the "Pearl of the Desert" - last May and it has since blown up Unesco-listed temples and looted relics that dated back thousands of years.

The city's recapture would be a strategic as well as symbolic victory for President Bashar al-Assad, since whoever holds it also controls the vast desert extending from central Syria to the Iraqi border, experts say.

Only some 15,000 of Palmyra's 70,000 residents stayed on under IS rule, which saw atrocities including public beheadings in the city's ancient amphitheatre, according to Observatory director Rami Abdel Rahman.

"The vast majority had already fled - only those too poor to flee stayed behind," he said.

The government's ground offensive, backed by Russian and Syrian warplanes, has been slowed by mines planted by IS in the fields surrounding the city, Abdel Rahman said.

Yet troops on Thursday appeared poised to launch their final assault on the city, as fighting raged on the edge of the Hayy al-Gharf neighbourhood in the southwest of the city.

"The army is 300 metres from the entrance of Palmyra," a Syrian military source told AFP on condition of anonymity.

A security source meanwhile said the army and its allies had closed in on Palmyra by recapturing three key hilltops around the city.

"Now the choice is in the hands of Daesh - either they withdraw or they will go to war in the city against the Syrian army. It is unlikely they will do the latter, because they have already started planting booby traps in the neighbourhoods," the source said.

Another security source said two army units backed by allied militia were taking part in the ground offensive.

The Observatory however reported IS was still deploying reinforcements to the frontlines.

Kerry in rare talks with Putin  

The focus of Syria's war has shifted to Palmyra since Russian President Vladimir Putin, a key Assad backer, last week announced a partial withdrawal of troops from Syria's war amid negotiations in Geneva between the regime and opposition.

In Moscow, US Secretary of State Kerry was to hold a rare meeting with Putin to gauge whether Russia is ready to discuss ways to ease ally Assad from power - a key demand of the Syrian opposition.

Lavrov first met his counterpart Sergei Lavrov, stressing that much work lay ahead.

"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.

Tuesday's bombings in Brussels "underscore the urgency" of fighting IS and other extremist organisations, he added.

The Moscow meetings came as UN envoy Staffan de Mistura met the government delegation to Geneva, on the final day in the current round of indirect peace negotiations.

Assad's future has been a key obstacle in the latest talks, with the government stubbornly insisting any discussion of him leaving is "excluded" and the opposition saying any talk of allowing him to stay is "absolutely unacceptable".

With the Geneva talks proving to be sluggish, all eyes are on Moscow since the two powers hold immense sway over the opposing sides in Syria's devastating conflict.

"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.

But in an interview with AFP, Damascus's lead negotiator at the Geneva talks Bashar al-Jaafari insisted that thinking that the regime could be pressured by its Russian ally was a "misreading" of the situation.

"When we say that the dialogue must be between Syrians, without outside intervention, this also applies to the Russians and Americans," he said.