KYIV (Reuters) - Moments after a Russian missile smashed into a Kyiv hospital where her infant son was being treated, Svitlana Kravchenko rushed to cover the two-month-old with a cloth to keep his airway clear.

"We heard the explosion, then we were showered with debris," recalled the 33-year-old after emerging from the hospital's bomb shelter, her voice quivering with fear and adrenaline.

Rescuers on Monday afternoon were still combing through the wreckage of the strike on Ukraine's largest children's hospital, hit in a barrage of missile strikes across the country that killed at least 29 people and wounded dozens.

The Russian military is waging an air campaign against Ukraine's critical infrastructure as its ground forces press forward along the front line of its 28-month-old invasion.

President Volodymyr Zelenskiy said Russia fired more than 40 missiles targeting different cities and damaging infrastructure, commercial and residential buildings.

Moscow's defence ministry said it had carried out strikes on defence industry targets and aviation bases.

At the Kyiv hospital, doctor Yevheniia Rokhvarg described an "extremely powerful" explosion that shattered the downtown building where Mayor Vitali Klitschko said 16 people were wounded.

"It blew out windows and doors, furniture was falling," she said.

After the strike, hundreds of local residents flocked to the hospital offering water and assistance. 

One woman stood crying outside the main gates, worried about a relative who had been inside.

Holding her baby son, Kravchenko stood outside with her husband Volodymyr, staring at the destruction. Their car had been buried under the rubble but the young family considered themselves lucky, as they had survived with just a few minor cuts.

Rokhvarg, a 55-year-old toxicology specialist, said all her immediate colleagues were alive, but that she was unsure about the fate of those who may have remained on the upper floors.

Asked whether she felt anger, she said she did not.

"Maybe exhaustion. And a very deep sadness," he said. "I just wish that this hadn't happened."

(Writing by Dan Peleschuk; Editing by Ros Russell)

By Max Hunder