Two Russian missiles have struck the eastern Ukrainian city of Kramatorsk and killed at least four people as rescue crews comb through a shattered restaurant in search of casualties.

The dead included a child while 42 people were injured at the restaurant, according to the city council in Kramatorsk, a city frequently targeted by Russian attacks. The second missile hit a village on the city fringes, injuring five.

A Russian missile also hit a cluster of buildings in Kremenchuk, about 375km west in central Ukraine, exactly a year after an attack on a shopping mall there that killed at least 20. No casualties were reported in the latest attack.

In Kramatorsk, emergency workers scurried in and out of the shattered restaurant on Tuesday as residents stood outside embracing, and surveying the damage.

The building was reduced to a twisted web of metal beams. Police and soldiers emerged with a man in military trousers and boots on a stretcher. He was placed in an ambulance, though it was not clear whether he was still alive.

Two men screamed in frenzied tones for a tow rope, then ran back towards the rubble.

“I ran here after the explosion because I rented a cafe here … Everything has been blown out there,” Valentyna, 64, told Reuters.

“None of the glass, windows or doors are left. All I see is destruction, fear and horror. This is the 21st century.”

Donetsk regional governor Pavlo Kyrylenko told national television people were visible under the rubble. Their condition was unknown, he said, but “we are experienced in removing rubble”.

Ukrainian President Volodymyr Zelenskiy said in his nightly video message the attacks showed that Russia “deserved only one thing as a consequence of what it has done – defeat and a tribunal”.

Earlier, Ukraine’s government reprimanded Kyiv mayor Vitali Klitschko after criticism of city officials over the state of bomb shelters following the deaths of three people locked out on the street during a Russian air raid.

The government said it had also approved the dismissal of the heads of two Kyiv districts and two acting heads of districts.

Uncertainty about the Kyiv mayor’s political future grew after Zelenskiy criticised officials in the capital over the June 1 incident, in which two women and a girl were killed by falling debris after rushing to a shelter and finding it shut.

Zelenskiy also ordered an audit of all bomb shelters in Kyiv after the incident, and said personnel changes would be made.

Prime Minister Denys Shmyhal told a government meeting the audit ordered by Zelenskiy had found 77 per cent of the shelters in Ukraine were fit for use, but many did not “meet any standards”.

He said the situation was “unacceptable” in some places, and mentioned districts in the Zaporizhzhia, Sumy, Zhytomyr and Kyiv regions as well as the city of Kyiv.

– AAP