The United Nations is unable to confirm reports that hundreds of Russian troops had crossed into Ukraine to shore up pro-Moscow rebels, the spokesman added.
Ban "is alarmed by reports that fighting in eastern Ukraine has spread southward, near the border of the Sea of Azov and the Russian federation", he said.
"If confirmed, this will mark a dangerous escalation in the Ukrainian crisis," he added.
The UN Security Council is to hold an emergency meeting from 1600 GMT on the crisis in Ukraine following NATO reports that over 1,000 Russian troops were fighting in Ukraine and an Ukrainian official described it as a "direct invasion" by Russia.
The UN chief called on Ukraine and Russia to return to talks on ending the four-month conflict that has left more than 2,200 dead and brought East-West relations to their lowest point since the end of the Cold War.