Russian troops are pressing toward Ukraine’s capital after a night of explosions and street fighting that sent Kyiv residents seeking shelter underground.

The country’s president refused an American offer to leave the city, insisting he would stay and adding: “The fight is here.”

It was not clear how far Russian troops had advanced. Ukrainian officials reported some success in fending off assaults, but fighting persisted near the capital.

Skirmishes reported on the edge of the city suggested small Russian units were probing Ukrainian defences to clear a path for the main forces.

Kyiv mayor Vitali Klitchsko said a missile hit a high-rise building near Zhuliany airport on the city’s south-western outskirts.

He posted an image showing a gaping hold in one side of the building that ravaged apartments on several floors. Firefighters said at least six civilians were injured by a rocket that hit the building, and 80 people were evacuated.

The swift movement of troops after less than three days of fighting further threatened a country clinging to independence in the face of a broad Russian assault, which threatened to topple Ukraine’s democratic government and scramble the post-Cold War world order.

Ukrainian President Volodymyr Zelensky offered renewed assurance on Saturday that the country’s military would stand up to the Russian invasion. In a video recorded in a central Kyiv street, he said he remained in the city.

“We aren’t going to lay down weapons. We will protect the country,” he 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.”

Mr Zelensky said in a second video later on Saturday that Moscow’s plan to quickly seize the capital and install a puppet government had been unsuccessful. In an emotional speech, he accused Russian forces of hitting civilian areas and infrastructure.

He also pushed for Ukraine’s urgent ascension to the European Union, saying he had discussed the issue with EU leaders.

US officials believe Russian President Vladimir Putin is determined to overthrow Ukraine’s government and replace it with a regime of his own.

The invasion represented his boldest effort yet to redraw the map of Europe and revive Moscow’s Cold War-era influence, and it triggered new international efforts to end the invasion, including direct sanctions on Mr Putin.

The Kremlin accepted Kyiv’s offer to hold talks, but it appeared to be an effort to squeeze concessions out of the embattled Mr Zelensky instead of a gesture towards a diplomatic solution.

The US government urged the Ukrainian leader early on Saturday to leave Kyiv but he turned down the offer, according to a senior American intelligence official, who quoted the president as saying that “the fight is here” and that he needed anti-tank ammunition but “not a ride”.

Saturday’s street clashes followed two days of massive air and missile strikes that Russian officials said targeted Ukrainian military facilities as their ground troops moved in from the north, east and south.

The assault pummelled bridges, schools and apartment buildings, and resulted in hundreds of casualties. Ukraine’s health minister reported on Saturday that 198 people had been killed and more than 1,000 wounded since the Russian offensive started before dawn on Thursday.

Viktor Lyashko said the death toll included included three children. His statement did not make clear whether the total figure included military and civilians.

City officials in Kyiv urged residents to seek shelter, stay away from windows and take precautions to avoid flying debris or bullets. Many spent the night in basements, underground parking garages and subway stations.

Zelensky adviser Mykhailo Podolyak said Ukrainian forces controlled the situation when small Russian units tried to infiltrate Kyiv. UK armed forces Minister James Heappey said fighting in the capital was so far confined to “very isolated pockets of Russian special forces and paratroopers” and that “the main armoured columns approaching Kyiv are still some way off”.

Russia’s defence ministry claimed its military had taken full control of the southern city of Melitopol, about 22 miles inland from the Azov Sea coast.

It was unclear how much of Ukraine was still under Ukrainian control and how much Russian forces had seized.

The US and other global powers moved to freeze the assets of Mr Putin and his foreign minister Sergei Lavrov on Friday as part of tougher sanctions on Russia as the invasion reverberated through the world’s economy and energy supplies.

Russia remained unbowed, vetoing a UN Security Council resolution demanding that it stop attacking Ukraine and withdraw troops immediately. The veto was expected, but the US and its supporters argued that the effort would highlight Moscow’s international isolation.

The 11-1 vote, with China, India and the United Arab Emirates abstaining, showed significant opposition to Russia’s invasion of its smaller, militarily weaker neighbour.

Nato decided to send parts of the alliance’s response force to help protect member nations in the east for the first time. The alliance did not say how many troops would be deployed but added that it would involve land, sea and air power.

Ukrainian officials claimed hundreds of Russians have died in the first days of fighting. Russian authorities released no casualty figures.UN officials said more than 120,000 Ukrainians have left the country for Poland, Moldova and other neighbouring nations. The UN estimates that up to four million could flee if the fighting escalates.

Late on Friday, US President Joe Biden signed a memo authorising up to 350 million dollars (£261 million) in additional security assistance to Ukraine, bringing the total security aid approved for Ukraine to a billion dollars (£740 million) over the past year. It was not clear how quickly the aid would flow.