Up to 2 million refugees could flee to Turkey if fighting intensifies in northwestern Syria as aid funds run dangerously low, the UN said Monday.

Syria's Russian-backed military has been pressing an assault on rebels in their last major stronghold with air attacks and ground battles that have ­already forced tens of thousands to leave their homes.

"Our fear is if this continues, and if the numbers continue soaring, and if the conflict intensifies, that we could see really hundreds of thousands, a million, two, heading toward the borders with Turkey," said Panos Moumtzis, the UN Regional Humanitarian Coordinator for the Syria Crisis.

The onslaught since late April, focused mostly on southern parts of Idlib province and adjacent parts of Hama and Latakia, marks the most intense conflict between President Bashar al-Assad and his insurgent enemies since last summer.

Moumtzis told Reuters in Geneva that the situation was deteriorating and a deal between Russia and Turkey to deescalate the fighting there was effectively no longer in place.

"We see an offensive that is really targeting - or with an impact on - hospitals and schools in civilian areas, in areas where there is the population and urban areas - which really should not be happening according to international humanitarian law," Moumtzis said.