Moscow (AFP) - Moscow on Friday proposed that Russia and United States, which have been flying separate bombing campaigns in Syria, launch joint air strikes against jihadists from next week, a proposal the Pentagon swiftly rejected.

"We are proposing to the US, as the head of the International Syria Support Group, to take part as of May 25 in joint operations between the Russian air force and the air force of the coalition," Russian defence minister Sergei Shoigu said in televised comments.

Shoigu said that the proposal included strikes against Jabhat al-Nusra and other illegal armed groups that do not support a frail truce brokered by Moscow and Washington in February.

He also proposed that joint strikes target "convoys containing weapons and ammunition (and) armed units that illegally cross the Syrian-Turkish border."

"We believe that adopting these measures will ensure the transition to a peace settlement process over all of Syria's territory," Shoigu said. "Of course, the leadership of the Syrian Arab Republic has agreed to these measures."

Pentagon spokesman Navy Captain Jeff Davis rejected Moscow's proposal, saying the US military does "not collaborate or coordinate with the Russians on any operations in Syria."

US State Department spokesman John Kirby said nothing had been agreed.

"What we are discussing with our Russian counterparts... are proposals for a sustainable mechanism to better monitor and enforce the cessation of hostilities," Kirby said.

He added that the "vast majority" of the violations of the truce had been carried out by the regime, which is backed by Moscow.

- Russia 'enabling' Assad -

"Russian operations are supporting and enabling the Assad regime and our focus is solely on degrading and defeating ISIL," Davis said, referring to the Islamic State jihadist group.

Davis added that the Pentagon had received "nothing formal" from its Russian counterpart regarding the proposal.

Russia and the United States pledged earlier this month to redouble efforts to find a solution to the Syrian conflict, which has killed more than 270,000 people and displaced millions since 2011, and extend a truce across the war-torn country.

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Despite diplomatic efforts to resolve the five-year conflict, Moscow and Washington have been critical of each other's bombing campaigns in Syria.

The West has accused Moscow -- a staunch supporter of Syrian President Bashar al-Assad -- of propping up the regime by targeting rebels fighting Assad in strikes Moscow said were aimed against "terrorist" organisations.

Moscow has in turn repeatedly slammed the US coalition, saying its strikes in Syria have been ineffective.

Shoigu said Friday that Russia would reserve its right to unilaterally strike "international terrorist and illegal armed groups that have not adhered to the cessation of hostilities" starting from May 25.

- Russian withdrawal? -

President Vladimir Putin surprised the West in March by announcing the partial withdrawal of Russian troops from Syria, saying Moscow's task in the war-torn country had been "on the whole" completed.

The Pentagon said Wednesday that Russia's military strength in Syria had barely changed since the partial withdrawal was announced.

Baghdad-based US military spokesman Colonel Steve Warren said that Russia had established some sort of forward operating base outside Palmyra, the ancient city Syrian forces recaptured in March from Islamic State jihadists with the help of Russian air strikes and special forces.

The Russian defence ministry denied that it was building a base in Palmyra, saying its military installations in the area are a "temporary camp" used for demining operations.

Meanwhile Hezbollah chief Hassan Nasrallah on Friday said his Lebanese Shiite movement would boost its support for Syria's regime after one of its top commanders was killed there last week.

According to Hezbollah expert Waddah Charara, the Shiite militant group has sent between 5,000 and 6,000 combatants to Syria since 2013.

Hezbollah has accused Islamist extremists of killing its commander Mustafa Badreddine in an artillery attack near Damascus. last week.