The United Nations refugee agency issued a warning about the deteriorating situation in Ukraine in face of Russia's invasion and urged neighboring countries to keep their borders open to civilians seeking asylum.

"We have already seen reports of casualties and people starting to flee their homes to seek safety," Filippo Grandi, U.N. high commissioner for refugees, said in a statement.

The United Nations High Commissioner for Refugees (UNHCR) said it had stepped up its operations and was working with Ukrainian authorities to provide greater humanitarian assistance. It was also working with governments in neighboring countries "calling on them to keep borders open to those seeking safety and protection," it said.

People in the southeastern city of Mariupol woke to the sound of explosions on Thursday and some started packing bags to leave after Russia invaded Ukraine.

Mariupol, eastern Ukraine's main port, was not attacked as the invasion began. But residents fear it could become a target for Russia as it is strategically important and only about 10 kilometers (6 miles) from areas controlled by pro-Russian separatists.

Ukrainian border guards said Thursday their country was coming under Russian artillery fire and land invasion along its northern border with Belarus as well as on its southern frontier.