Kyiv, Mar 8: Minor progress has been made on establishing safe corridors to allow civilians to escape the fighting.
A top Ukranian official says both sides agreed to a 12-hour-long cease-fire on Tuesday for the evacuation of civilians from a key eastern city.
Meanwhile, Russian aircraft continued to bomb cities in eastern and central Ukraine overnight, Ukrainian officials said.
Shelling pounded suburbs of the capital, Kyiv.
Ukrainian President Volodymyr Zelenskyy is urging his people to keep resisting the assault, which United Nations officials say has forced more than 1.7 million to flee the country.
Ukraine's foreign minister says more than 20,000 people from 52 countries have volunteered to fight in Ukraine.
As the war enters its 13th day, food, water, heat and medicine have grown increasingly scarce in Ukraine.
Here's a look at key things to know about the war:
Has there been progress on safe evacuations?
The Russian coordination center for humanitarian efforts in Ukraine said Russia will begin a cease-fire at 10 am Moscow time (0700 GMT) Tuesday to allow civilians to flee through special corridors that the Russians say was agreed upon with Ukrainian authorities, according to Russian media.
Most of those corridors would lead to Russia either directly or via Belarus, according to officials in Moscow.
However, Russia's ambassador to the UN suggested that humanitarian paths leading from the capital, Kyiv, and other cities could give people choice in where they want to go.
Ukrainian Deputy Prime Minister Iryna Vereshchuk said on Tuesday both sides agreed to a cease-fire from 9 am to 9 pm Ukraine time (0700 to 1900 GMT) for the evacuation of civilians from the eastern city of Sumy.
Those being evacuated from Sumy include foreign students from India and China, she said.
The Russian Defense Ministry has said civilians will be allowed to leave Sumy, Mariupol and Kyiv.
In the southern port city of Mariupol, an estimated 200,000 people nearly half its population are hoping to flee. Hospitals there are facing severe shortages of antibiotics and painkillers.
Ukrainian and Russian officials held a third round of direct talks Monday since the start of invasion February 24.
The countries' foreign ministers are scheduled to meet in Turkey on Thursday, according to that country's top diplomat.
What else is happening on the ground?
In the capital, soldiers and volunteers have built hundreds of checkpoints to protect the city of nearly 4 million people, often using sandbags, stacked tires and spiked cables.
A Russian general was killed in the fighting in Ukraine's second-largest city, according to the Ukrainian military intelligence agency.
He was identified as Maj. Gen. Vitaly Gerasimov the second Russian general reportedly killed since the invasion began.
The report said he had fought with Russian forces in Syria and Chechnya and had taken part in the seizure of Crimea in 2014. It was not possible to confirm the death independently. Russia has not commented.
The mayor of Lviv said the city in far western Ukraine is struggling to feed and house the tens of thousands of people who have fled there from war-torn regions of the country.
More than 200,000 Ukrainians displaced from their homes are now in Lviv, filling up sport halls, schools, hospitals and church buildings.
Russian aircraft bombed cities in eastern and central Ukraine overnight, Ukrainian officials said. Shelling pounded suburbs of the capital, Kyiv. In Sumy and Okhtyrka, to the east of the capital near the Russian border, bombs fell on residential buildings and destroyed a power plant, a regional leader said. Bombs also hit oil depots in two other towns.
Russian troops have overall made significant advances in southern Ukraine but stalled in some other regions.
A top US official said multiple countries were discussing whether to provide the warplanes that Ukraine's president has been pleading for.
How many people have been killed?
The death toll of the conflict has been difficult to measure. The UN human rights office said Monday that it had confirmed the deaths of 406 civilians and wounding of 801 others through the end of Sunday.
However, it acknowledged the actual figures are likely considerably higher.
The World Health Organisation said it verified at least six attacks that have killed six health care workers and injured 11 others.
Ukrainian refugees continue to pour into neighbouring countries, including Poland, Romania and Moldova. Among them are an unknown number of people with US citizenship, though some haven't been able to flee Ukraine yet.
Surging prices for oil and other vital commodities, such as wheat used in subsidized bread and noodles, are rattling global markets.
The situation remains uncertain as investors search for safe havens from expanding sanctions against Russia.
Worries are growing that Russia's invasion of Ukraine will upend already tight supplies of oil.
Russia is one of the world's largest energy producers, with prices surging even further by the possibility the US might bar crude imports from Russia.
A growing number of multinational businesses have cut Russia off from vital financial services, technology and a variety of consumer products in response to Western economic sanctions and global outrage over the war.
Among those suspending services in Russia due to sanctions is Netflix, the popular streaming service.
In the Middle East, the war in Ukraine is magnifying divisions in the region following Moscow's role in recent years in the war in Syria and among militant factions in Lebanon, Iraq and Yemen where ally, Iran, has influence.
Despite countries sending weapons and military equipment to Ukrainian forces fighting the Russians, Western countries have rejected Ukrainian calls to impose a no-fly zone over the country. There are concerns such a move would risk dramatically escalating the conflict. (AP)