Marine General Joseph Dunford, the chairman of the US military's Joint Chiefs of Staff, told Congress on Thursday that the Pentagon had no intention of forging an intelligence sharing arrangement with Russia.

US Defense Secretary Ashton Carter (L) and Chairman of the Joint Chiefs of Staff Joseph Dunford testify before a Senate Armed Services Committee hearing in Washington, September 22, 2016. (Reuters photo)

"I do not believe it would be a good idea to share intelligence with the Russians," he told the Senate Armed Services Committee while testifying with US Defense Secretary Ashton Carter.

Dunford said any such coordination between the US and Russia against ISIS would be extremely limited.

US Republican Senator John McCain, the chairman of the Senate Armed Services Committee, fiercely criticized the possibility of future cooperation and called US Secretary of State John Kerry, who brokered a collapsed ceasefire agreement in Syria, "delusional" for seeking it.

"It would mean that the US military would effectively own future Russian airstrikes in the eyes of the world," McCain said.

The comments come amid increasing tensions between the US and Russia over Monday’s deadly strike on a humanitarian aid convoy near the city of Aleppo. Both sides blame each other for the attack.

Meanwhile, Moscow has rejected a proposal by Washington which calls on Russia and Syria to stop flying their warplanes over Syria’s battle zones.

A truce engineered by Washington and Moscow effectively collapsed after reports emerged of a US airstrike on Syrian soldiers in the east of the country and another attack coming from an unknown source targeting a humanitarian convoy in the northwestern city of Aleppo.

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