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Syrian rebels and local officials pursued talks with regime ally Russia on Sunday over the fate of the key southern region of Daraa, currently facing a ferocious regime offensive, according to local media.

The Free Syrian Army, part of the opposition, denied any agreement with the Russians had yet been reached.

Rebel spokesman Ibrahim Jabawi told local media on Sunday that the Russians had realised that the previous day's talks  had broken down because they were dictating the terms of surrender, not negotiating with the opposition.

The Jordan-backed talks came as a tentative calm reigned over most fronts in Daraa, which has been subjected to daily air assaults for almost two weeks, according to the Syrian Observatory for Human Rights.

A "ceasefire has largely held since Saturday at 7:00 pm (1600 GMT) to facilitate the ongoing negotiations," Observatory chief Rami Abdel Rahman said.

On Saturday, negotiations between the opposition and the Russian brokers broke down when the rebels rejected the conditions put forward by Russia for them to surrender.

"The talks collapsed because the Russians insisted on their conditions that want us to surrender," Jabawi said on Saturday.

"The [rebels'] negotiating team refused to surrender and refused to accept the Russian conditions," he added.

Since June 19, Russia-backed regime forces have ramped up bombardment against opposition fighters in southern Syria as Damascus pushes to retake the area.

The region borders Jordan and the Israeli-occupied Golan Heights and is considered to be the cradle of the uprising against President Bashar al-Assad seven years ago that sparked the civil war.

The regime has chipped away at rebel-held territory in Daraa since the escalation began almost two weeks ago.

Most fronts were quiet Sunday with the exception of areas near Tafas in Daraa's northwest hit by regime airstrikes, the Observatory said.

Clashes between rebels and regime forces in the same area killed four opposition fighters, it said.

Russia is seeking the rebel handover of heavy and medium-sized weapons, and the deployment of Russian military police and Syrian police into towns retaken by government forces, Abdel Rahman said.

Damascus and Moscow are pushing for a deal that would see regime forces take over the Naseeb border crossing with Jordan and deploy along the frontier with the Golan Heights, he said.

An AFP correspondent outside Daraa city - part of which is held by rebels - said Saturday night had been quiet, with only intermittent bombardment.

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After retaking control of eight towns under Russia-mediated deals on Saturday, Assad's regime now controls more than half of Daraa province, up from just 30 percent before the escalation, according to the Observatory.

State news agency SANA said Sunday the national flag had been hoisted in one of these towns, Dael, while Syrian state television showed images of people celebrating.

Regime forces have retaken large parts of the country lost to rebels since Russia intervened on its behalf in 2015.

The conflict has killed more than 350,000 people and displaced millions since it started in 2011.

Agencies contributed to this report.