A senior UN official has warned that open warfare may erupt in eastern Ukraine once again, following reports of Russian tanks and troops crossing the border.

"We are deeply concerned by the possibility of a return to full-scale fighting," Assistant Secretary-General Jens Anders Toyberg-Frandzen told an emergency meeting of the UN Security Council.

The meeting was requested by the United States after NATO said columns of Russian tanks, artillery and troops had entered eastern Ukraine in the past two days.

Russia denied the claims.

More than 930,000 people have been driven from their homes in the fighting, and the UN official warned that "the numbers could grow exponentially" with a surge in violence.

"Alternatively, the conflict may simmer in this way for months with sporadic low-level battles marked by periods of increased hostilities and casualties," Mr Toyberg-Frandzen said.

He added both scenarios spell "catastrophe for Ukraine."

The UN official raised a third prospect of a "frozen and protracted conflict that would entrench the status quo in southeastern Ukraine for years or several decades to come."

The 15-member council has no plans to adopt a resolution condemning Russia, which has veto power.

It was the 26th meeting called by the Security Council to address the crisis.