Ukraine forces have ended a rebel blockade of a strategic airport in the east, killing at least 30 rebels, as the country traded charges and threats with Russia, over violations of their joint border during a weekend of fierce military combat.

Ukraine's military said on Monday that its warplanes had inflicted heavy losses on the pro-Russian separatists during air strikes on their positions around Luhansk airport. An armoured convoy, which Kiev said had crossed the border from Russia, was also hit.

Government forces, taking the lead from Ukrainian President Petro Poroshenko who swore to "find and destroy" the separatists who killed 23 servicemen in rocket strikes on Friday, went on the offensive across a broad range of targets at the border town of Luhansk.