A purported satellite image shows Russian arms near Debaltseve, Ukraine. (Courtesy of Geoff Pyatt)

A new cease-fire between Ukrainian troops and pro-Russian rebels held together Sunday relatively unscathed except in the one place it may matter most: the area around Debaltseve, site of the heaviest recent fighting.

Sounds of artillery fire and shelling over Debaltseve could be heard clearly Sunday from a stretch of highway about 20 miles to the northwest. The city, a rail hub, has been under siege for weeks as pro-Russian separatists effectively surrounded it, hampering the evacuation of civilians and, more recently, all but trapping about 5,000 pro-Kiev troops inside.

Each side blamed the other for violations of the cease-fire agreement in the area Sunday, in the hours after the deal went into effect at midnight. Although international observers noted that Debaltseve seemed to be one of just a few exceptions to an otherwise functional cease-fire, the continued shelling in the war’s most critical theater struck many on the ground as a sign that the truce might not hold for long.

“This cease-fire won’t amount to anything — they’ll have a break and regroup their forces,” said Anatoly Hromovoy, 46, a senior lieutenant and one of the first to escape Debaltseve after the cease-fire, in a convoy of wounded and dead soldiers. “It’s going to be a huge fight. It can get worse. Debaltseve wasn’t yet a massacre.”

On the eve of the cease-fire, rebel leader Alexander Zakharchenko had warned in comments to Russian news agency Interfax that the separatists did not consider Debaltseve to be part of the peace agreement and pledged to “block all attempts” by soldiers to break out of the city unless they agreed to surrender.

Ukrainian officials don’t see it that way. They argue that Debaltseve is not exempted from the deal that the leaders of Ukraine, Russia, Germany and France struck in Minsk, Belarus, last Thursday after all-night negotiations. Ukraine’s National Security and Defense spokesman in Kiev also maintained Sunday that the Ukrainian side still controls the main road leading out of Debaltseve, although soldiers who made a run for Ukraine-controlled territory in the hours after the cease-fire told a slightly different story.

“The road wasn’t blocked, but it was constantly under heavy fire,” said Artyom Maximov, 31, who was brought out early Sunday on a medical convoy. “They shot at us, but we weren’t hit. They missed us in the fog.”

Northwest of the city, the roads were mostly empty, except for the Ukrainian soldiers at checkpoints or those walking freely between military vehicles lined up in stretches along the roadside. Occasionally, heavy military vehicles — including an armored personnel carrier and a multiple-rocket launcher — sped by from the direction of Artemivsk, a city that has served as a triage point for wounded soldiers and escaping civilians, going in the direction of Debaltseve. Their destination was not clear.

Ukrainian President Petro Poroshenko and pro-Russian rebel leaders ordered their fighters to hold fire just after midnight Sunday, bringing a tenuous pause to fighting that had been rapidly escalating in recent days, with violence ratcheting up particularly strongly since the two sides agreed Thursday to the midnight deadline.

Poroshenko also warned that Ukraine would respond to any purported violations. In the days leading up to the cease-fire, he reserved the right to impose martial law “across Ukraine” if the deal were broken. He noted that he was in touch with President Obama about how to coordinate a response to any escalations, according to his spokesman Svyatoslav Tsegolko’s Twitter account.

Over the weekend, the Obama administration released satellite images that it said showed the Russian army had joined the pro-Russian separatists in their efforts to encircle Debaltseve and take the city, supplying artillery systems and multiple-rocket launchers to the area. It was impossible to independently verify the grainy black-and-white satellite images posted to Twitter by the U.S. ambassador, Geoffrey Pyatt.

Poroshenko also noted Saturday that Russia had taken a particular interest in Debaltseve during the Minsk negotiations last week.

Russia has denied that it is a party to the conflict, and its foreign ministry suggested that Ukraine and the United States had “distorted” the meaning of the agreement.

Under the terms of the truce, Ukraine and pro-Russian rebels agreed to pull their heavy weaponry back 30 to 85 miles from the front lines. Ukraine also committed to end an economic blockade of rebel-held territories and give them greater powers of self-rule. The parties also committed to remove foreign fighters from Ukrainian territory, and give Ukraine full control of its borders by the end of 2015.

Rebel leader Zakharchenko said that if separatists are not satisfied with how Kiev upholds the bargain, they will seize more territory in eastern Ukraine.

The 10-month-old conflict has cost at least 5,400 lives, according to U.N. estimates, and displaced more than a million people.

Alexander Pustovit, and Michael Birnbaum in Moscow, contributed to this report.