The United States and European Union have voiced concern over reports of large convoys of troops and weapons moving through territory controlled by pro-Russian rebels in eastern Ukraine.
The White House said any attempt by the rebels to seize more territory would be a "blatant violation" of a September 5 cease-fire agreement.
National Security Council spokesperson Bernadette Meehan also urged Russia to stop arming the rebels and withdraw all its troops and weapons from Ukraine.
A similar warning was also issued by EU foreign policy chief Federica Mogherini.
Moscow denies sending arms or troops into eastern Ukraine where some 4,000 have died since April.
On November 8, the Organization for Security and Cooperation said its monitors had spotted an armored column of troops without insignia heading west on a highway near the rebel-held city of Donetsk.
Ukraine said it had no doubt the new troops were Russians.
Military spokesman Andriy Lysenko said its standoff with the Russian-backed separatists has intensified in the past week.
His comments came after reports of intensive shelling in and around the city of Donetsk overnight and into the morning of November 9.
Lysenko said Ukraine's military believes Russia could stir up tension to provide a pretext to "send in so-called Russian peacekeeping units."
Ukraine has accused Russia of sending a column of 32 tanks and truckloads of troops into the country's east to support the pro-Russian rebels in recent days.
Meehan said the White House was "very concerned" by the intensified fighting and reports of the separatists moving large convoys of weapons and tanks to the front lines.
"Any attempt by separatist forces to seize additional territory in eastern Ukraine would be a blatant violation of the Minsk agreements," Meehan said in a statement, referring to the cease-fire deal reached in the Belarus capital on September 5.
Mogherini called the reports of rebel convoys "a very worrying development."
Demanding all parties adhere to the September 5 cease-fire and seek a solution that would respect Ukraine's territorial integrity, Mogherini urged Russia to "fully assume its responsibilities in this regard."
That means "preventing any further movement of military, weapons or fighters from its territory into Ukraine, and withdrawing any troops, weapons and equipment under its control from Ukraine," she said.
Russian Foreign Minister Sergei Lavrov said on November 8 that he had "no information" about Russian troops or tanks being in eastern Ukraine.
A rebel commander has also denied Moscow has sent fresh arms or troops.
Eduard Basurin, a rebel commander in Donetsk, said the separatists were only moving fresh fighters to the front line.
"We have to rotate some of our formations," Basurin told Russia's Ria Novosti news agency.