"Eighteen died -- eight men and 10 women. At the moment, we are still digging through the rubble," the Odessa regional administration said in a statement.

The attack came on the first day of an invasion of Ukraine that President Vladimir Putin launched after sparring for weeks with the West about NATO's presence in eastern Europe.

It was the deadliest single strike so far of the day reported by Ukrainian officials, who had earlier put the death toll across the country at around 50, including about 10 civilians.

The attack struck a military base about 100 kilometres (62 miles) north of Odessa, in a region near Ukraine's border with Moldova.