KYIV, Ukraine — Kyiv residents braced Saturday for another night sheltering underground, as Russian troops closed in on Ukraine’s capital and skirmishes were reported on the outskirts. Ukraine’s leader, meanwhile, vowed to continue fighting the Russian assault as he appealed for more outside help.

“The real fighting for Kyiv is ongoing,” President Volodymyr Zelenskyy said in a video message in which he accused Russia of hitting infrastructure and civilian targets.

“We will win,” he said.

Central Kyiv appeared quiet on Saturday, though sporadic gunfire could be heard. And fighting on the city’s outskirts suggested that small Russian units were trying to clear a path for the main forces. Britain and the U.S. said the bulk of Russian forces were 19 miles (30 kilometers) from the center of the city.

As Russian troops pressed their offensive with small groups of troops reported inside Kyiv, the city’s mayor, Vitali Klitschko, extended an overnight curfew to run from 5 p.m. Saturday until 8 a.m. on Monday, saying any civilians out past curfew “will be considered members of the enemy’s sabotage and reconnaissance groups.”

Russia claims its assault on Ukraine is aimed only at military targets, but bridges, schools and residential neighborhoods have been hit since the invasion began Thursday with air and missile strikes and Russian troops entering Ukraine from the north, east and south.

Ukraine’s health minister reported Saturday that 198 people, including three children, had been killed and more than 1,000 others had been wounded during Europe’s largest land war since World War II. It was unclear whether those figures included both military and civilian casualties.

In Kyiv, a missile struck a high-rise apartment building in the southwestern outskirts near one of the city’s two passenger airports, leaving a jagged hole of ravaged apartments over several floors. A rescue worker said six civilians were injured.

The conflict has driven thousands of Ukrainians from their homes in search of safety. U.N. officials said more than 120,000 Ukrainians had left the country for Poland, Moldova and other neighboring nations.

Zelenskyy reiterated his openness to talks with Russia in a video message Saturday, saying he welcomed an offer from the leaders of Turkey and Azerbaijan to organize diplomatic efforts, which so far have faltered. A day earlier, Zelenskyy offered to negotiate a key Russian demand: to abandon its ambitions of joining NATO.

Russian President Vladimir Putin sent troops into Ukraine after he spent weeks denying that’s what he intended, all the while building up a force of almost 200,000 troops along the countries’ borders. He claims the West has failed to take seriously Russia’s security concerns about NATO, the Western military alliance that Ukraine aspires to join. But he has also expressed scorn about Ukraine’s right to exist as an independent state.

Putin has has not disclosed his ultimate plans for Ukraine but Western officials believe he is determined to overthrow Ukraine’s government and replace it with a regime of his own, redrawing the map of Europe and reviving Moscow’s Cold War-era influence.

It was unclear in the fog of war how much territory Russian forces have seized. Britain’s Ministry of Defense said “the speed of the Russian advance has temporarily slowed likely as a result of acute logistical difficulties and strong Ukrainian resistance.”

A senior U.S. defense official said Saturday that more than half of the Russian combat power that was massed along Ukraine’s borders had entered Ukraine, and that Russia has had to commit more fuel supply and other support units inside Ukraine than originally anticipated. The official, who spoke on condition of anonymity to discuss internal U.S. assessments, did not provide further details.

Ukraine’s Infrastructure Ministry said a Russian missile was shot down before dawn Saturday as it headed for the dam of the sprawling water reservoir that serves Kyiv, and Ukraine said a Russian military convoy was destroyed near the city early Saturday. Footage showed soldiers inspecting burned-out vehicles after Ukraine’s 101st brigade reported destroying a column of two light vehicles, two trucks and a tank. The claim could not be verified.

Highways into Kyiv from the east were dotted with checkpoints manned by uniformed Ukrainian troops and young men in civilian clothes carrying automatic rifles. Low-flying planes patrolled the skies, though it was unclear if they were Russian or Ukrainian.

In addition to Kyiv, the Russian assault appeared to focus on Ukraine’s coastline, which stretches from near the Black Sea port of Odesa in the west to beyond the Azov Sea port of Mariupol in the east.

If the Russian troops succeed, Ukraine would be cut off from access to all of its sea ports, which are vital for its economy. In Mariupol, Ukrainian soldiers guarded bridges and blocked people from the shoreline amid concerns the Russian navy could launch an assault from the sea.

Fighting also raged in two territories in eastern Ukraine that are controlled by pro-Russian separatists. Authorities in the city of Donetsk said hot water supplies to the city of about 900,000 were suspended because of damage to the system by Ukrainian shelling.

The U.S. government urged Zelenskyy early Saturday to evacuate Kyiv but he turned down the offer, according to a senior American intelligence official with direct knowledge of the conversation. Zelenskyy issued a defiant video recorded on a downtown Kyiv street early Saturday, saying he remained in the city.

“We aren’t going to lay down weapons. We will protect the country,” the Ukrainian president said. “Our weapon is our truth, and our truth is that it’s our land, our country, our children. And we will defend all of that.”

Hundreds of thousands of Ukrainians have been on the move, seeking safety in the west of the country or beyond. The U.N. estimates that up to 4 million could flee if the fighting escalates.

Refugees arriving in the Hungarian border town of Zahony said men between 18 and 60 were not being allowed to leave Ukraine.

“My son was not allowed to come. My heart is so sore, I’m shaking,” said Vilma Sugar, 68.

Hungary and Poland both opened their borders to Ukrainians. At Poland’s Medyka crossing, some said they had walked for 15 miles (35 kilometers) to reach the border.

“They didn’t have food, no tea, they were standing in the middle of a field, on the road, kids were freezing,” said Iryna Wiklenko as she waited on the Polish side for her grandchildren and her daughter-in-law to make it across.

Officials in Kyiv urged residents to seek shelter, to stay away from windows and to take precautions to avoid flying debris or bullets. Many spent Friday night in basements, underground parking garages and subway stations, and prepared to do the same on Saturday.

Shelves wore thin at some Kyiv grocery stores and pharmacies, and some worried how long stockpiles of food and medicine might last.

The U.S. military announced $350 million in assistance to Ukraine on Saturday, including anti-tank weapons, body armor and small arms. Germany likewise said it would send missiles and anti-tank weapons to the country.

The U.S. and its allies have beefed up troops on NATO’s eastern flank but so far have ruled out deploying troops to fight Russia.

Instead, the U.S., the European Union and other countries have slapped wide-ranging sanctions on Russia, freezing the assets of Russian businesses and individuals including Putin and his foreign minister.

Zelenskyy appealed for tougher sanctions, urging holdout countries in Europe to agree to cut Russia out of the SWIFT international payments system.

A senior Russian official on Saturday shrugged off the sanctions as a reflection of Western “political impotence.”

Dmitry Medvedev, the deputy head of Russia’s Security Council, warned that Moscow could react to the sanctions by opting out of the last remaining nuclear arms pact, freezing Western assets and cutting diplomatic ties with nations in the West.

“There is no particular need in maintaining diplomatic relations,” Medvedev said. “We may look at each other in binoculars and gunsights.”