VIDEO: Ukrainian President refuses to flee as Russian troops storm toward capital

Russian troops stormed toward Ukraine’s capital early on Saturday as explosions reverberated through the city and the president urged the country to "stand firm” against the siege that could determine its future. He refused American help to evacuate, saying: "The fight is here.”

Hundreds of casualties were reported in the fighting, which included shelling that sliced through a Kyiv apartment building and pummeled bridges and schools. There also were growing signs that Russia may be seeking to overthrow Ukraine’s government, which US officials have described as Russian President Vladimir Putin’s ultimate objective.

The assault represented Putin's boldest effort yet to redraw the world map and revive Moscow’s Cold War-era influence. It triggered new international efforts to end the invasion, including direct sanctions on Putin.

As his country confronted explosions and gunfire, and as the fate of Kyiv hung in the balance, Ukraine President Volodymyr Zelenskyy appealed for a cease-fire and warned in a bleak statement that multiple cities were under attack.

"This night we have to stand firm,” he said. "The fate of Ukraine is being decided right now.”

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137 killed, 316 hurt as Russia presses invasion to outskirts of Ukrainian capital

Zelenskyy was urged to evacuate Kyiv at the behest of the US government but turned down the offer, according to a senior American intelligence official with direct knowledge of the conversation. The official quoted the president as saying that "the fight is here" and that he needed anti-tank ammunition but "not a ride.”

For their part, US defence officials believe the Russian offensive has encountered considerable resistance and is proceeding slower than Moscow had envisioned, though that could change quickly.

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

The Russian military continued its advance, laying claim Friday to the southern Ukraine city of Melitopol. Still, it was unclear in the fog of war how much of Ukraine is still under Ukrainian control and how much or little Russian forces have seized.