The United States on Sunday expressed alarm over the increased fighting in eastern Ukraine and reports of a new wave of military reinforcements that recently made its way into the region from neighboring Russia.

Bernadette Meehan, spokesperson for the U.S. National Security Council, stressed the need for compliance to the Minsk ceasefire agreement, noting that such was the best chance of reaching a lasting accord on the conflict.

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Meehan warned pro-Russia separatists against taking further action that would constitute a violation of the ceasefire jointly signed by representatives from Ukraine, Russia, Donetsk and Luhansk in Minsk on Sept. 5.

The security council spokesperson also reminded Russia of its undertaking to end all military supply to rebels and pull out its troops and weapons from the region. She called on Moscow to aid efforts in bringing back Ukraine's sovereignty and in facilitating the release of prisoners.

The Organization for Security and Cooperation in Europe (OSCE) reported that two unmarked convoys carrying heavy artillery and missile launchers crossed the eastern Ukraine border this weekend.

However, Donetsk People's Republic militia deputy commander Eduard Basurin said the convoys were operated by "independence supporters" and were being moved for "tactical reasons."

On Friday, Ukraine accused Russia of deploying additional tanks, weapons and troops into the country's rebel-held eastern region.

Russia's Foreign Minister Sergei Lavrov, who was in Beijing to attend the Asia Pacific Economic Cooperation (APEC) leaders' summit, scoffed at the allegations.

Even the U.S. State Department's Jen Psaki said there was not enough information to back such reports, Lavrov said.

"Well, if Psaki doesn't have it, I don't," Lavrov added.

Earlier, Lavrov sat down with U.S. Secretary of State John Kerry where both agreed to share information on the Russia-Ukraine border crisis.

While Kerry later admitted there were some disagreements with regard to events that occurred in Ukraine, Lavrov welcomed Washington's involvement and called it a "step in the right direction."

Tagsrussia-ukraine, U.S., increased shelling, Ukraine ceasefire, Donetsk, APEC, John Kerry, Sergei Lavrov