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 neighborhood, while Russian forces took partial control of three northwest suburbs 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 24 hours shelling the already devastated southern port city of Mariupol from offshore.

Civilians making the dangerous escape from Mariupol 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."

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:

WHY ARE SUBURBS IN UKRAINE TURNING INTO BATTLEFIELDS?

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.

WHAT'S BEEN HAPPENING IN MARIUPOL?

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

Electricity, water and food supplies have been cut off, as well as communication with the outside world. It's unclear how many remain in the city with a prewar population of 430,000. About a quarter were believed to have fled early in the war and tens of thousands more have escaped over the past week by way of humanitarian corridors.

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.

"There are no buildings there anymore," said 77-year-old Maria Fiodorova, who fled to Poland.

"They bombed us for the past 20 days," said Viktoria Totsen, 39, who also 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."

WHAT HAS THE AP DIRECTLY WITNESSED OR CONFIRMED?

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.

WHAT ARE RUSSIA'S LATEST MILITARY MOVES?

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.

The official said that in contrast, the U.S. did not see indications that ships in the northern Black Sea were firing on Odesa, as they did over the weekend. The official said the U.S. believes Russia has about 21 ships in the Black Sea and about seven in the Azov Sea.

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.

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," Pentagon spokesman John Kirby said the U.S. has seen no evidence to suggest that such an escalation is imminent.

— Associated Press writers Lolita C. Baldor in Washington and Jill Lawless in London contributed to this report.

HAVE THERE BEEN NEW DIPLOMATIC TALKS?

Talks have been ongoing, but Ukrainian President Volodymyr Zelenskyy 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 Zelenskyy 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."

WHATS THE LATEST ON SANCTIONS AGAINST RUSSIA?

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.

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