Ukraine struggled to maintain a tenuous cease-fire with pro-Russian rebels after a series of repeated breaches Sunday, even as the government here faced the equally daunting task of selling the peace plan to the nation.

Firefights broke out near the rebel-held city of Donetsk as well as east of the key port city of Mariupol, eyewitnesses said. Yet Ukrainian officials maintained that in general, the truce, which went into effect Friday evening, was holding.

“The Ukrainian government still believes in the cease-fire ­despite the violations,” said Volodymyr Poleviy, deputy spokesman for Ukraine’s National Security Defense Council.

At the same time, President Petro Poroshenko faced the growing challenge of selling the deal to Ukrainians, some of whom may think that his government, confronting overwhelming force in the east, is suing for peace largely on Russian terms. The deal came together last week after a major new offensive by the rebels, who, according to NATO and Ukrainian officials, are being aided not only by Russian arms but also by Russian troops — ­charges that Moscow denies.

Ukrainians fear that the deal may ultimately leave the industrialized eastern regions of Ukraine in Moscow’s political sphere. Yuriy Lutsenko, one of Poroshenko’s senior advisers, seemed to acknowledge just that in a highly candid assessment Sunday, comparing post-truce Ukraine to the former East Germany and West Germany.

Those living in rebel-held territory centered on the eastern city of Donetsk, he suggested, would in time grow envious of the new prosperity in the western half of the country as it underwent reforms and received investment from the United States and Europe.

“When our standard of living is attractive, even to the Kremlin-poisoned citizens of Donetsk, we will open the door to anyone who recognizes an integrated and unified European Ukraine,” Lutsenko wrote on his Facebook page.

Apparently seeking a ray of light for Kiev, Lutsenko additionally claimed that during the NATO summit last week, Poro­shenko had reached a deal with five Western nations — the United States, Poland, Italy, Norway and France — to provide weapons, equipment or military advisers. But officials from at least four of those nations objected to that characterization.

The United States, Ukraine and other nations will be conducting joint military exercises in the Black Sea this week, and Washington has already pledged $60 million in nonlethal assistance to Kiev. But the Obama administration has drawn the line at lethal assistance, and one U.S. official familiar with the situation said Sunday that despite Ukrainian claims, “our position remains the same.”

Officials from Poland, Italy and Norway told Reuters that the report was incorrect — although Italy, at least, has promised to supply helmets and bulletproof vests.

On Sunday, the full 12-point cease-fire agreement was finally published, two days after it was signed in Minsk, Belarus. The brevity of the deal — it covered only 11 / 2 pages of text — underlined just how much work remains to be done for a stable peace to be achieved. The core of the deal, however, appeared to be based on an outline for peace personally drafted by Russian President Vladimir Putin, and included broad amnesty as well as prisoner exchanges and monitoring of the Ukraine-Russia border.

The document offered few specifics about the central issue facing Ukraine: the political future of the separatist regions. But it hinted at potentially significant concessions, including a pledge to implement “decentralization of power” in the restive east and the adoption of a law granting a “temporary procedure of local self-governance in certain areas of Donetsk and Luhansk regions.”

Ukraine and the rebels, however, have differed sharply on what decentralization of power would look like on the ground, with the Ukrainian government in Kiev rebuffing demands for broad autonomy.

On Sunday, fears were growing among a segment of Ukrainians that Kiev may be bending to Moscow’s will, potentially creating a frozen conflict zone in the east similar to the breakaway regions in Georgia and Moldova that are sustained by Russian interventions.

“This is an absurd plan, and no one will go for it,” said a 20-year-old businessman turned soldier from Donetsk who gave his name only as Oleg in order to talk freely. He has been fighting since May in one of the volunteer militia units set up by the government in Kiev to bolster its armed forces. Since then, he said, he has watched six of his comrades die in combat with pro-Russian rebels.

Oleg said he and other pro-Ukrainian residents in the east would feel deeply betrayed if the truce ultimately left rebel “criminals” in charge. “I have watched my friends and relatives die in this conflict. That cannot have been for nothing,” he said.

And yet, the cease-fire itself appeared to be less a truce than a scaling down of violence.

Poleviy said that rebel forces had launched limited rocket attacks on Ukrainian military positions beginning late Saturday and continuing into Sunday. Officials in the eastern city of Mariupol said one woman was killed and three were wounded in fighting overnight. The Ukrainian-military-held airport in the rebel-controlled city of Donetsk also came under fire. “We hope it was the product of miscommunications,” Poleviy said.

But there were also signs of limited progress. Ukrainian officials said Sunday that prisoner swaps agreed to as part of the truce had begun Saturday, with two privates from the 9th Battalion of Ukraine’s territorial defenses released at a checkpoint in the eastern Luhansk region.

Boris Litvinov, chairman of the Supreme Council of the Donetsk People’s Republic, one of the main rebel groups, said skirmishes had broken out after the cease-fire but would not say which side was instigating the violations. But he charged the Ukrainian military with using the truce to bolster its positions with additional troops and equipment in the east.

“The truce is on paper, but the battles are continuing,” he said in a telephone interview. “I don’t want to be a prophet, but I am sure that in the next day the Ukrainian army will start attacking again, but we do not want more causalities.”

Birnbaum reported from Moscow. Karoun Demirjian in Moscow, Alex Ryabchyn in Kiev and Craig Whitlock in Tbilisi, Georgia, contributed to this report.