The United States has rejected a proposal by Russia to conduct joint airstrikes against Daesh terrorists in Syria from next week, but did not rule out the possibility of discussing ways to better monitor an existing ceasefire in the war-torn country.

"We do not collaborate or coordinate with the Russians on any operations in Syria," Pentagon spokesman Navy Captain Jeff Davis told reporters on Friday.

Davis said that the US and Russia are pursuing separate military objectives, claiming that "Russian operations are supporting and enabling the (Bashar al-) Assad regime and our focus is solely on degrading and defeating ISIL."

Since September 30, 2015, Russia has been conducting airstrikes against Daesh and other terrorist groups in Syria at the Syrian government’s request.

The strikes have killed hundreds of Daesh terrorists and other foreign-backed militants and inflicted heavy material damage on them.

Since September 20014, the US and its allies have also been carrying out airstrikes in Syria purportedly against Daesh positions. However, the Syrian government has charged that the airstrikes had targeted the country's infrastructure in many instances and done little to stop the advances of terrorists.

Earlier on Friday, Russian Defense Minister Sergei Shoigu said that the two countries should carry out joint airstrikes against Jabhat al-Nusra and other armed groups that do not support a truce reached by Moscow and Washington to facilitate negotiations between warring sides to the conflict.

On Friday, Russian Defense Minister Sergei Shoigu suggested that the US and Russia carry out joint strikes against Jabhat al-Nusra and other armed groups in Syria. (File photo)

Shoigu also called for joint strikes to be conducted against "convoys containing weapons and ammunition, armed units that illegally cross the Syrian-Turkish border."

He said that such operations would begin as of May 25 and be coordinated with the Syrian government.

"We believe the adoption of these measures will allow a transition to a peaceful process to be achieved in the entire territory of Syria," he said. "Of course, these measures have been coordinated with the leadership of the Syrian Arab Republic."

Davis said Moscow had not made a formal proposal to the United States. "I've only seen the same press reports you have -- nothing formal has been presented to us."

The Syria truce, which went into effect late February and excludes Daesh militants and al-Nusra Front, is still officially in place in many parts of Syria despite surging violence in Aleppo.

Last week, top diplomats from 17 nations resumed Vienna talks on the Syria conflict, hoping to reinvigorate a peace effort that has effectively collapsed.

(L to R) US Secretary of State John Kerry, Russian Foreign Minister Sergei Lavrov, UN Special Envoy for Syria Staffan de Mistura talk during press conference after talks in Vienna, Austria, May 17, 2016. (AFP photo)

US Secretary of State John Kerry and Russian Foreign Minister Sergei Lavrov were chairing the meeting of the International Syria Support Group (ISSG) on Tuesday.

State Department spokesman John Kirby said Friday that "what we are discussing with our Russian counterparts -- in keeping with the ISSG communique last week in Vienna -- are proposals for a sustainable mechanism to better monitor and enforce the cessation of hostilities."

"None of those proposals have yet been agreed upon," Kirby added.

Syria has been gripped by militancy since March 2011. Damascus has long been saying that Saudi Arabia, Turkey and Qatar are funding and arming anti-Syria terrorist groups, including Daesh terrorists.

UN special envoy for Syria Staffan de Mistura estimates that over 400,000 people have been killed in the conflict, which has also displaced over half of the Arab country’s pre-war population of about 23 million.