DONETSK, Ukraine (CNN) -

A few miles south of the town of Starobeshevo in eastern Ukraine, a group of men in uniform is slumped under a tree.

They are dejected and exhausted, their eyes red with fatigue.

They do not want to be filmed but tell us of the horror they endured a day earlier. As medics with the Ukrainian army, they had transported the bodies of some 70 soldiers away from a combat zone and many more who were seriously wounded.

They scarcely raise their heads when a Ukrainian air force jet streaks across the sky, releasing its payload on a rebel-held area to the east. It's the only action by the air force that we've witnessed against a rebel force that's suddenly gone on the offensive across a wide area of eastern Ukraine.

Ukrainian President Petro Poroshenko warned Saturday that the crisis with Russia has worsened in recent days and is inching closer to a "full-scale war."

Border guard bases and checkpoints deserted

The drive north from the port city of Mariupol -- only a couple of miles from the Russian border -- offered no evidence of a Ukrainian presence. Bases of the border guard service are deserted, checkpoints on rural roads abandoned, sandbags strewn along the verge. In effect, Ukraine has forfeited control of perhaps as much as 200 miles of its eastern border.

The Ukrainians claim that Russian artillery fired from across the border is helping the rebels advance and that thousands of Russian troops are mixed in with the separatists. Moscow denies both claims.

Certainly the rebel forces, now united under the banner of Novorossiya -- or New Russia -- are better armed and organized than they were two months ago. They have at least some T-72 tanks; many carry new weapons. And after spending months on the defensive, they are suddenly buoyant.

By contrast, a small detachment of Ukrainian troops we encountered on the way north seemed demoralized. One asked when the British Army would arrive to help Ukraine in its desperate need; another gloomily predicted a rebel onslaught at any moment.

When we finally reached Starobeshevo, a rebel checkpoint had been hastily erected at the edge of town. The men were sunburned and relaxed, waving us through without even checking documents, a rarity in a country where both sides relish leafing through passports.

The town itself fell to the pro-Russian separatists Friday, part of an advance south that has encircled the remnants of the Donbass Battalion, a volunteer militia fighting alongside government forces. Several houses had been badly damaged and at least one was destroyed by a direct hit.

Locals said Ukrainian fire was to blame, but there is no way to prove it. The shrapnel cut jagged holes in the metal fence of the modest home opposite and damaged the roof.

The elderly couple who lived there seemed shocked by the violence that had erupted around their rural community. The husband, Victor, said he was pure Ukrainian but accused the government of lying to the people.

"The Ukrainians came like peacekeepers," he said, "but then they kill us. They're destroying the whole Donbass region."

But Victor, who is 80, isn't about to be run out of the town where he was born.

An eerie quiet in Donetsk

As we finished speaking with Victor, a battered black sedan with a flak jacket hanging over the driver's door pulled up, and a NovoRossiya fighter got out. He told us we must stop filming unless we could show press accreditation. But accreditation could be obtained only in Donetsk, a city not so easy to enter now with the Ukrainian army shelling it. Soon the fighter's commander was on the scene, a tall man in his early 40s with an air of natural authority.

"You know I can just take away your camera," he said.

We were not in a position to argue. Instead he put two of his men in our minivan and dispatched us with an escort to Donetsk, some 30 miles away. As the vehicle raced across open country, they trained their Dragonov rifles out of the window, whether for show or because Ukrainian units were still in the area was unclear.

After a few minutes at the State Security building in Donetsk, now the military headquarters of the separatists, we were allowed to go but advised not to leave the city until our accreditation was in order. In any case, trying to leave Donetsk in the late afternoon, when the shelling and rocket fire picks up, didn't seem the smartest idea.

Compared with two months ago, the city is eerily quiet. The outdoor cafes and parks that were crowded in the early summer are deserted and more stores are boarded up. Shells have hit the stadium of the football club, Shakhtar, and wrecked apartment buildings.

It seems most of the people who are still here are those with nowhere else to go, caught in the middle of a war that threatens to lurch into the bitterly cold winter.