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

Weapons fell silent in war-torn eastern Ukraine early Sunday as government troops and pro-Russian rebels started a cease-fire, with initial reports from across the region suggesting that the truce was largely holding despite doubts about its durability.

On Saturday, rebel leader Alexander Zakharchenko told the Interfax news agency that rebel forces planned to cease hostilities everywhere “except Debaltseve” — ordering pro-Russian forces to “block all attempts to break out” of the city, saying the agreement struck Thursday in Minsk between Ukrainian, Russian, French and German leaders didn’t mention Debaltseve by name.

The announcement led Ukrainian President Petro Poroshenko to issue a caveat to his cease-fire order, delivered live on Ukrainian television just after midnight Sunday, should the rebels make good on their threat to keep up the offensive at Debaltseve.

“I see now only one threat: When the rebels were shelling residential areas in Debaltseve,” Poroshenko said. “If they hit us in one cheek, we will not turn the other. May God forgive me.”

Both sides reported violations, although the cease-fire generally appeared to be holding.

Rebels said they had responded to fire from Kiev forces in Debaltseve two hours after the truce started. Ukrainian forces, meanwhile, said one of their checkpoints in Zolote, 25 miles north of Debaltseve, had been shelled by rebels.

In comments leading up to his cease-fire order, Poroshenko noted that Russia had shown a particular interest in the Debaltseve area during the marathon cease-fire negotiations in Minsk. Ukrainian and U.S. officials have asserted that separatists used the 2 1 /2-day window to try to seize Debaltseve, where up to 8,000 Ukrainian soldiers are said to be trapped.

On Saturday, the Obama administration released a series of satellite images that it said showed the Russian army had joined the rebels in a full-scale assault to surround troops in the area around the city. Russia has denied that it is a party to the conflict, and it was impossible to verify the three grainy black-and-white satellite images posted to Twitter by the U.S. ambassador to Ukraine, Geoffrey Pyatt.

According to the United States, the images, commissioned from the private Digital Globe satellite company, showed artillery systems and multiple-rocket launchers Thursday in the area near Debaltseve.

“We are confident these are Russian military, not separatist, systems,” Pyatt tweeted. Early Saturday night, the steady, rumbling sound of shelling in Debaltseve could be heard in the center of Artemivsk, a city that has served as a triage point for wounded soldiers and escaping civilians as fighting in Debaltseve has worsened. A few hours earlier, Artemivsk had come under shelling for the second time in as many days — though this time, no one was killed.

In the final two hours before the cease-fire deadline, a fog rolled in and the city went quiet, save for a few couples marking Valentine’s Day in a relatively empty Japanese restaurant and pensive men in military fatigues, many carrying assault rifles, pacing the halls of hotels and the hospital or attempting to calm themselves with a beer in the city’s one open pizza joint.

“No one gets in, and no one gets out,” said Bogdan, a sergeant who commands a 60-member unit in Chornukhyne, a suburb of Debaltseve, in the lobby of the Hotel Ukraina. He came to Artemivsk from the front about a week ago because of some minor injuries, he said, but now, unable to return because of the rebel movements, he has been calling his men every two hours to check how badly they are surrounded.

When asked about his hopes for the cease-fire, Bogdan snorted.

“I don’t believe in it,” he said. “I don’t believe in Santa Claus, either.”

Few soldiers believe there is any hope for the cease-fire to hold, and some are ready to dole out blame all around.

“Russia takes what it wants, even though we have the capability to fight back,” said Igor, 24, a former infantryman who is now a minesweeper. He dropped his rifle on the floor with a clang and pushed a beer aside to brandish a set of armor-piercing bullets his unit recently found on former rebel territory — ammunition he said could only have come from Russia.

“It is so much worse than what they show on television,” said Vitaly, 28, his colleague, complaining that most of the information about the conflict is “Ukrainian propaganda or Russian propaganda” — and that all of it plays down the seriousness of the situation at the front.

“If they say seven or eight are dead, it’s really 70 or 80,” Vitaly said. “They’re sending people into the field with no protection and no place to hide.”

Earlier Saturday, a Ukrainian military spokesman said that seven soldiers had been killed and 23 wounded in the previous 24 hours.

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

Intense shelling was also reported Saturday near the rebel stronghold city of Donetsk and east of the key government-held port of Mariupol.

A pro-Kiev militia said Saturday that a town five miles east of Mariupol had been “virtually wiped out during an artillery battle.”

The rebels’ multiple-rocket launcher systems were hitting Shyrokyne, near Mariupol, “uninterruptedly,” the far-right nationalist volunteer Azov Battalion wrote on its social media account.

Rebels control only a portion of the Donetsk region. But they warned on Saturday that if they are not satisfied that Kiev is upholding its commitments under the Minsk agreement to give them strong powers of autonomy, they will try to conquer more territory.

“If our demands about de facto independence are not fulfilled, we will declare that the whole territory of Donetsk region is ours,” said Zakharchenko, the rebel leader, according to Russian news agencies. “It doesn’t matter by what means it is seized. If it doesn’t work by political means, we have shown that it is possible in another way.”

In the peace deal, Ukraine and the rebels committed to pull heavy weaponry 30 to 85 miles from the front lines. Ukraine also said it would end an economic blockade of rebel-held territories and offer the areas broad powers of self-rule. A commitment was made to pull foreign fighters from Ukrainian territory, and Ukraine is to receive full control of its border by the end of the year.

But on Saturday, the Russian Foreign Ministry warned in a statement that Ukraine and the United States have “begun to distort the content of the Minsk agreements.”

Poroshenko said that he had spoken to President Obama on Saturday and that they agreed on “further coordination of efforts in case of escalation,” Poroshenko’s spokesman Syvatoslav Tsegolko wrote on Twitter.

If the cease-fire is broken, he said, martial law would be imposed “across Ukraine.”