Russian forces inched towards Kyiv Saturday and pounded civilian areas in other Ukrainian cities as concerns grew over the besieged southern port of Mariupol, where officials said more than 1,500 people had been killed, according to AFP.

Air raid sirens sounded Saturday in several cities, including the capital Kyiv, Odessa, Dnipro and Kharkiv, according to Ukrainian media.

More than two weeks after Moscow started its military operation in Ukraine, the United Nations and others said it may be committing war crimes in cities such as Mariupol, which for days has been under attack by Vladimir Putin's forces.

Survivors have been trying to flee a freezing city left without water or heating and running out of food. The situation is "desperate," a Doctors Without Borders official said.

"Hundreds of thousands of people... are for all intents and purposes besieged," Stephen Cornish, one of those heading the medical charity's Ukraine operation, told AFP in an interview.

"Sieges are a medieval practice that have been outlawed by the modern rules of war for good reason."

Ukrainian President Volodymyr Zelensky said they were trying to arrange evacuations from besieged cities but Russian forces were disrupting efforts.

"Mariupol remains blocked by the enemy. Russian troops did not let our aid into the city and continue to torture our people, our Mariupol residents," Zelensky said in a video address late Friday.

"Tomorrow we'll try again. Once again, send food, water and medicine to our city."

As talks between Moscow and Kyiv seemingly go nowhere, Zelensky's pleas for NATO to intervene have grown increasingly desperate.

Washington added more layers of sanctions to those already crippling Russia's economy, this time ending normal trade relations and announcing a ban on signature Russian goods vodka, seafood and diamonds.

The United States and the European Union also suspended the export of their luxury goods to Russia.

"Putin must pay the price. He cannot pursue a war that threatens the very foundation of international peace and stability and then ask for help from the international community," US President Joe Biden said from the White House.

He spoke as the United Nations said 2.5 million people had now fled Ukraine and around two million more had been internally displaced by the war.