Updated

At least two Ukrainian troops have been killed Tuesday amid an ongoing assault against pro-Russian rebels in the eastern city of Slovyansk, according to a spokesman for the country’s anti-terror operation.

Vladyslav Seleznev told Fox News that 40 Ukrainian troops and dozens of rebels have also been injured in the clashes.

Ukraine’s interior minister, Arsen Avakov, said Tuesday that government troops broke through rebel positions around the village of Semenovka on the eastern fringe of Slovyansk. "An active offensive stage of the counterterrorist operation is underway in Slovyansk," he wrote on his Facebook page.

Avakov warned residents in Slovyansk and nearby cities of Kramatorsk and Krasny Liman to stay at home.

An AP journalist just south of Slovyansk heard sustained gun and artillery fire and saw plumes of black smoke rising over the city.

A Ukrainian military officer, who spoke on condition of anonymity because he wasn't authorized to speak to the media, said one serviceman was killed and 13 others were wounded when their vehicle came under rebel fire near Slovyansk.

The Interfax news agency quoted rebels in Slovyansk as saying that the government used combat jets and helicopter gunships as well as artillery to bombard their positions.

Ukrainian authorities have repeatedly announced an escalation in armed operations, only to eventually back down. Government forces have in recent days been noticeably reinforced to the north of Slovyansk, however, and deployment of air power over the past week has signalled increased determination.

Slovyansk, which sits on a strategic highway, has seen daily fighting between government forces and the rebels, who have seized government buildings and set up checkpoints around the eastern provinces of Donetsk and Luhansk that form Ukraine's industrial heartland.

The fighting has escalated following the May 25 presidential election won by billionaire candy magnate Petro Poroshenko, with rebels launching an attack on Donetsk airport and shooting down a government helicopter over Slovyansk.

On Monday, hundreds of rebels armed with automatic weapons and rocket-propelled grenades mounted a daylong siege of a border guards base on the outskirts of Luhansk that coordinates the protection of Ukraine's border with Russia. Border guards said they killed at least five rebels in repelling the attack.

Fox News’ Greg Palkot and The Associated Press contributed to this report.