The strike on the shipbuilding town about 35 km (22 miles) northwest of the front line in Kherson came as Russia ordered 60,000 people to flee the region "to save your lives" in the face of a Ukrainian counter offensive.
Russian Defence Minister Sergei Shoigu discussed the "rapidly deteriorating situation" in phone calls with British, French and Turkish counterparts, the ministry said.
He also spoke by phone with US Defense Secretary Lloyd Austin for the second time in three days. The Pentagon said Austin told Shoigu he "rejected any pretext for Russian escalation."
Shoigu said Ukraine could escalate by using a "dirty bomb", or conventional explosives laced with radioactive material.
Ukrainian Foreign Minister Dmytro Kuleba rejected the accusation, as "absurd" and "dangerous", adding: "Russians often accuse others of what they plan themselves."
In a joint statement after the talks, Britain, France and the United States said they were committed to supporting Ukraine "for as long as it takes" and rejected Russia's warning about a "dirty bomb".
"Our countries made clear that we all reject Russia’s transparently false allegations that Ukraine is preparing to use a dirty bomb on its own territory," they said.
"The world would see through any attempt to use this allegation as a pretext for escalation."
Sunday's missile strike in Mykolaiv wiped out the top floor of the apartment block, sending shrapnel and debris across a plaza and into neighbouring buildings, a Reuters witness said No fatalities were recorded.
"After the first blast, I tried to get out, but the door was stuck," said Oleksandr Mezinov, 50, who was woken from his bed by the blasts. "After a minute or two, there was a second loud blast. Our door was blown into the corridor."
On Sunday, Ukraine's General Staff said anti-aircraft defences had shot down 12 of Russia's Iranian-made Shahed-136 attack drones in the past 24 hours.
Tehran denies supplying the weapons to Russia.
Ukraine's advances in recent weeks around Kherson and in the country's northeast have been met with intensifying Russian missile and drone attacks on civilian infrastructure, which have destroyed about 40 per cent of Ukraine's power system ahead of winter.
Russian troops have withdrawn from parts of the front and occupation authorities are evacuating civilians deeper into Russian-held territory before an expected battle for Kherson, the regional capital on the west bank of the Dnipro river.
Kherson is a gateway to Crimea, which Russia annexed in 2014.
"The situation today is difficult. It's vital to save your lives," Russian Education Minister Sergei Kravtsov said in a video message. "It won't be for long. You will definitely return."
Russia-installed authorities there reported insufficient vessels to ferry people across the river at one point on Sunday, blaming a "sharp increase in the number of people wishing to leave".
About 25,000 people have been evacuated since Tuesday, the Interfax news agency said.
Ukraine's military said it was making gains in the south, taking over at least two villages it said Russia had abandoned.
Russia's defence ministry said on Sunday its forces had kept up attacks on Ukraine's energy and military infrastructure, destroyed a large ammunition depot in the central Cherkasy region, and repelled Ukrainian counter-offensives in the south and east.
Ukrainian President Volodymyr Zelenskiyy said the Russian attacks on energy infrastructure had struck on a "very wide" scale.
With the war about to start its ninth month and winter approaching, the potential for freezing misery loomed.
Volodymyr Kudritskiy, head of Ukraine's national energy company, Ukrenergo, said power had been restored to more than 1.5 million customers after mass weekend attacks on energy targets.
Moscow has acknowledged targeting energy infrastructure but denies targeting civilians in what it calls a "special military operation" in Ukraine.
Ukraine also accused Russia of hampering a deal on grain exports via the Black Sea, saying its ports were working only at 25 per cent to 30 per cent capacity.
The pact, brokered by the United Nations and Turkey in July, paved the way for Ukraine to resume grain exports from Black Sea ports that had been shut since Russia invaded.
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