The battle for Ukraine’s cities thundered across its suburbs Tuesday, with the Ukrainian military saying it forced Russian troops out of a strategically important Kyiv suburb, while Russian forces took partial control of three northwest areas where there’s been fighting for weeks.

A senior U.S. defense official said Tuesday that Russian ground forces were still largely stalled outside the capital city, but Russian ships spent the past day shelling the already devastated southern port city of Mariupol from offshore.

Thousands of civilians made the dangerous escape from Mariupol on Tuesday. Some described fleeing through street gun battles and past corpses as Russian forces tried to pound the city into submission. One woman who made it out said planes flew overhead “and dropped bombs everywhere.”

Ukraine’s Deputy Prime Minister Iryna Vereshchuk said about nine humanitarian corridors were agreed upon for Wednesday.

The Kyiv city administration says Russian forces shelled the Ukrainian capital overnight and early Wednesday morning, damaging buildings in two districts. Four people suffered injuries.

There was no word of a diplomatic breakthrough. Ukraine’s President described negotiations with Russia as “step by step, but they are going forward.” The U.S. intends to announce new sanctions against Russia this week. Meanwhile, more than 3.5 million people have fled Ukraine since the war began Feb. 24, and millions more have been displaced within the country, the United Nations said.

Here are some key things to know about the conflict:

The suburbs could be a barrier to Ukraine’s cities or a doorway for Russian troops, particularly around the capital of Kyiv — believed to be Moscow’s primary military objective.

After a fierce battle, Ukrainian troops regained control of the suburb of Makariv on Tuesday, allowing Ukrainian forces to retake a key highway to the west and block Russian troops from surrounding the capital from the northwest, Ukraine’s Defense Ministry said.

But the ministry said Russian forces were able to partially take northwest suburbs of Bucha, Hostomel and Irpin, some of which had been under attack for weeks.

John Kirby, the Pentagon’s spokesman, said the U.S. was not in a position to confirm that Ukrainian troops regained Makariv, but said, “we have seen indications that the Ukrainians are going a bit more on the offensive now.”

The Russian assault has turned life in Mariupol into a fight for survival.

Electricity, water and food supplies have been cut off, as well as communication with the outside world.

During his nightly address to the nation, Ukrainian President Volodymyr Zelensky accused Russian forces of blocking a humanitarian convoy trying to bring desperately needed supplies to Mariupol and seizing what another Ukrainian official said were 15 of the bus drivers and rescue workers on the aid mission. Zelensky said the Russians had agreed to the route ahead of time.

Although people continued to evacuate Mariupol in droves, Zelensky said about 100,000 remain in the city in “inhuman conditions”and under constant shelling and bombardment. The prewar population of the port city was 430,000.

Many attempts to leave have been thwarted by Russian efforts to pound Mariupol into submission. On that, Moscow has not succeeded, Britain’s defense ministry said Tuesday. But Russia now controls the land corridor from Crimea, the peninsula it annexed in 2014, and is blocking Ukraine’s access to the Sea of Azov.

Those who have made it out of Mariupol described a devastated landscape.

“They bombed us for the past 20 days,” said Viktoria Totsen, 39, who fled to Poland. “During the last five days the planes were flying over us every five seconds and dropped bombs everywhere — on residential buildings, kindergartens, art schools, everywhere.”

Explosions and bursts of gunfire shook Kyiv, and heavy artillery fire could be heard from the northwest, where Russia has sought to encircle and capture several the capital’s suburban areas. Black smoke could be seen at a distance in the north.

In Lviv, families exchanged tearful farewells as women and children boarded trains to Poland while men of fighting age stayed behind, barred from leaving the country. An air raid siren could be heard blaring over the city.

A senior U.S. defense official, who spoke on condition of anonymity to provide the U.S. military assessment, said Tuesday that Russian ships in the Sea of Azov have been shelling Mariupol from offshore over the last day.

According to the official, Russian ground forces were still largely stalled outside Kyiv. And, the official said, Russia is struggling to get food and fuel to its troops. There are indications that some troops don’t have proper cold-weather gear and are suffering from frostbite.

A Western official, who spoke on condition of anonymity to discuss intelligence matters, said Ukraine’s resistance has slowed Russia’s advance almost to a halt, but Russian troops have not retreated. Kremlin spokesman Dmitry Peskov denied that Russia’s invasion has stalled. He instead insisted that the military operation was going “strictly in accordance with the plans and purposes that were established beforehand.”

A day after U.S. President Joe Biden reiterated accusations that Putin is considering use of chemical or biological weapons, saying Putin’s “back is against the wall,” Kirby, the Pentagon spokesman, said the U.S. has seen no evidence to suggest that such an escalation is imminent.

In a separate worrying development, Russian military forces destroyed a laboratory that is responsible for improving management of radioactive waste at the Chernobyl nuclear power plant. The laboratory contained “highly active samples” that are “now in the hands of the enemy,” the Ukrainian state agency responsible for the Chernobyl exclusion zone said in a statement Tuesday.

Biden plans to announce new sanctions against Russia on Thursday while he is in Brussels for meetings with NATO and European allies, White House national security adviser Jake Sullivan said. He declined to provide details.

Several major corporations have been cutting business ties with Russia in recent weeks. French energy giant TotalEnergies said Tuesday that it will halt all purchases of Russian oil and petroleum products by the end of 2022. The company said in a statement that it will “gradually suspend its activities in Russia” and stressed “the existence of alternative sources for supplying Europe” with oil.

Talks have been ongoing, but Ukrainian President Volodymyr Zelensky has not been granted a direct meeting with Putin, as he has requested.

Zelenskyy has said he would be prepared to consider waiving any bid by Ukraine to join NATO — a key Russian demand — in exchange for a cease-fire, the withdrawal of Russian troops and a guarantee of Ukraine’s security.

The Kremlin is demanding Ukraine disarm and declare itself neutral. Russian presidential spokesperson Dmitry Peskov said Tuesday that he could not share details of ongoing talks, saying that making them public would damage negotiations.

U.N. Secretary-General Antonio Guterres said “elements of diplomatic progress are coming into view on several key issues.” He said the gains are enough to end hostilities now. He gave no details.

French President Emmanuel Macron talked with both Putin and Zelensky on Tuesday about a potential cease-fire, according to a statement from the French presidency. They reached “no agreement,” the statement said, but Macron “remains convinced of the need to continue his efforts” and he “stands alongside Ukraine.”