The eastern Ukrainian city of Kramatorsk was hit by Russian strikes early Tuesday, after Moscow's forces said they were shifting their military aims to target the east of the country.

Kramatorsk has largely been spared destruction witnessed by other east Ukraine cities, like the country's second-largest settlement Kharkiv, since Russia invaded last month.

An AFP journalist in the city said one of the strikes at around 3:00 am local time (0000 GMT) had destroyed a school in the centre, located near a police station.

The strikes left a large smouldering crater about 10 metres wide next to the damaged school building, the journalist said, and many windows of the building were blown out in the attack.

There was no official confirmation of deaths or injuries but residents nearby said the school was empty at the time and no-one had been hurt in the attack.

Ukraine authorities warned recently they expected fighting in eastern Ukraine to worsen after Moscow pulled forces from around the capital Kyiv to focus on the "liberation" of the eastern Donbas region.

Thousands of residents of Kramatorsk, which had an approximate pre-war population of 150,000, have been taking trains west to flee an anticipated increase in fighting.

Officials said on Tuesday morning that evacuations by train were being halted while any damage was being assessed to rail tracks outside the city.

Several Russian missile attacks struck Kramatorsk in the early days of the invasion, which began in late February, including an attack that targeted the airport.

The strikes overnight Monday to Tuesday were the first in the city centre in several weeks.