Ukrainian officials said Russia’s proposal on Monday to open "humanitarian corridors" for cities in Ukraine is not a genuine offer because it offers to evacuate civilians only to Belarus and Russia.

Iryna Vereshchuk, a Ukrainian vice prime minister, in a televised briefing called that "unacceptable" and said Ukraine had demanded instead that civilians be allowed to evacuate to other parts of Ukraine.

Russia’s Defense Ministry had said it would open a corridor from towns and villages north of Kyiv, where heavy fighting is taking place, but that would allow people to travel to the Belarusian city of Gomel and then be flown to Russia. Russia also offered corridors near the besieged northeastern and eastern cities of Kharkiv, Sumy and Mariupol, but that would also only allow people to leave over the border to Russia.

"This is an unacceptable option of humanitarian corridors. Our people from outskirts of Kyiv won’t go to Belarus and then to Russia," Vereshchuk said.

She said that Ukraine wants civilians north of Kyiv to be permitted to leave to the capital and for those from Kharkiv to be allowed to western cities by train, and from Mariupol north to the central city of Zaporizhzhia.

"We delivered our proposal on how the corridors should be organized," Vereshchuk said, later adding, "Humanitarian aid is prepared for a number of towns in the east and south. We ask Russia to confirm these corridors and provide ceasefire."

Russia has repeatedly violated its own ceasefire since offering humanitarian corridors for Mariupol and another eastern town Volnovakha, including shelling evacuation points in Mariupol according to officials there. The Red Cross, which is trying to organize the evacuations, has said the agreements currently are too vague and without clear understandings for routes out.

Russia said Monday's offer for the corridors was made following a lengthy phone conversation between French President Emmanuel Macron and Russian President Vladimir Putin on Sunday.

Vereshchuk said Russia was trying to exploit Macron’s name for a disingenuous offer of corridors.

"I hope president Macron understands that his name and good intentions are manipulated by Russia," she said.

-ABC News’ Patrick Reevell

More than 1 million people fleeing Ukraine have arrived in Poland since the Russian invasion began on Feb. 24, the Polish Border Guard said on Monday.

A record 142,000 people arrived on Sunday, the guard said on Twitter. On Monday, about 42,000 people had crossed the border before 7 a.m. local time.

As of Sunday, more than 1.5 million people had fled the war in Ukraine, marking the "fastest growing refugee crises in Europe since World War II," according to Filippo Grandi, the U.N. high commissioner for refugees.

Russian forces have attacked Ukrainian communications infrastructure to "reduce Ukrainian citizens' access to reliable news and information," the U.K. Ministry of Defence said on Monday.

"Russia reportedly struck a TV tower in Kharkiv yesterday, suspending broadcasting output," the Ministry’s update said.

Russian forces on March 1 struck a TV tower in Kyiv, the capital.

Russia declared a cease-fire starting Monday morning, opening humanitarian corridors for the evacuation of civilians from Kyiv, Mariupol, Kharkiv and Sumy, the Russian interagency humanitarian response staff in Ukraine said.

"Taking into account the disastrous humanitarian situation and its severe deterioration in the cities of Kyiv, Kharkiv, Sumy, and Mariupol, and also at French President Emmanuel Macron's personal request to Russian President Vladimir Putin, the Russian Armed Forces are declaring a ceasefire and opening humanitarian corridors for reasons of humanity starting 10:00 a.m. on March 7, 2022," the staff said.

Ukrainian officials in Mariupol said Russia broke planned cease-fires on Saturday and Sunday. Russia's announcement on Monday of humanitarian corridors was "unacceptable," a Ukrainian official said, saying all of Russia's planned routes led to Russia.

U.S. Secretary of State Antony Blinken crossed the border into Ukraine Saturday after meeting with Ukrainian Foreign Minister Dmytro Kuleba at the Korczowa Border Crossing Point.

"The entire world stand with Ukraine," Blinken said, and Kuleba added that he hopes Ukrainians will see this as a "clear manifestation that we have friends who literally stand by us."

Blinken said the sanctions imposed so far against Russia are "producing very, very concrete results" and that the pressure will "grow" until this "war of choice is brought to an end."

When asked directly about helping Kuleba with more firepower, Blinken said, "the support for Ukraine not only has been unprecedented, not only is going to continue, it's going to increase."

Kuleba said Ukraine "appreciates" sanctions that have been announced in the last week, but that more economic and political pressure and "necessary weapons," would "save many lives in Ukraine... many sufferings will be avoided."

Kuleba also said that they are “satisfied" with already arranged supplies of anti-tank weapons and ammunition, but that “it’s no secret” they still want fighter jets and air defense systems.

He also thanked the U.S. for sending stingers, and said they were used on Saturday.

"Just today we shot down three Russian attack aircrafts, which were bombing our cities with the use of stingers but we need -- so to say -- big air defense systems to ensure the safety of our skies. If we lose the skies, there will be much, much more blood on the ground,"Kuleba said.

In response to questions about NATO’s refusal to impose a no-fly zone over Ukraine, Kuleba said it’s a "sign of weakness," but stayed optimistic that they will change their minds.

"The time will come," he said.

-ABC News' Conor Finnegan and Justin Gomez