As sporadic firefights continued between Ukrainian troops and separatists, the government announced Monday that it was deploying police officers to the east and would fire those who refuse to go.

Interior Minister Arsen Avakov said in a statement that he was sending in the police out of necessity and as “a test of proficiency, spirit and patriotism.” He said their willingness to serve in the east will help instill trust in the institution, long seen as corrupt. Avakov said he had fired 21 police officers from the city of Chernihiv on Sunday because they refused to go, while 86 obeyed the directive.

Avakov did not indicate whether the officers would be sent to the front lines in the self-proclaimed “people’s republics” controlled by pro-Russian separatists. But he said that if ordered into combat, the officers would be provided with appropriate ammunition and body armor.

Deploying police from across Ukraine to the east will buttress regular army units, which have often struggled to repel rebel advances. Ukraine’s military has been weakened in recent years, starved of cash and training under the previous government. In part, that was a byproduct of the now-discredited belief that the country faced no imminent military threat.

The police, who report to the Interior Ministry, could be more supportive of the government in Kiev than at least some of the police officers serving in the east. The Organization for Security and Cooperation in Europe (OSCE) has said that in Luhansk, for example, the police force is split on whether to cooperate with the separatists.

The reinforcements will arrive at a time when lawlessness in the eastern regions appears to be increasing. They have been beset by criminal activity, with local authorities reluctant to intervene. However, it is difficult to know whether separatist fighters are to blame for the lawlessness or whether some of it is a symptom of the general unrest.

Last week, an armored bank vehicle carrying cash was robbed at gunpoint by men in camouflage near Donetsk . There was a report Monday of 20 armed men attempting to break into a factory in Donetsk that makes radio and electronic equipment for military use. A lawyer and a newspaper editor in the Luhansk region were kidnapped Sunday.

Meanwhile, OSCE monitors said guards in state prisons in the east have been abandoning their posts, leaving uncertain the fate of 23,000 inmates — some of whom are thought to be infected with tuberculosis.

Nonetheless, Donetsk and Luhansk were calm Monday, and the markets teemed with shoppers.

In Slovyansk, however, government troops and separatists exchanged fire at two checkpoints, said military spokesman Vladislav Seleznev. Troops were fired on with mortars and automatic weapons, he said, and shots were aimed at a military convoy and at civilian cars.

A pattern has developed, Seleznev said, of separatists ambushing government troops and then fleeing “into the swamps and forests.” He said rebels are clearly monitoring troop movements.

Seleznev also said that the army is trying to negotiate the release of six captured Ukrainian soldiers who were paraded before reporters Sunday in Slovyansk.

A video of the news conference showed the soldiers introduced by a man who identified himself as a former officer in the Ukrainian army who is now a deputy commander in the Donetsk People’s Republic army. The soldiers looked sullen and subdued as they sat at a table with their hands clasped in front of them. They said they were being held in cells but were being treated humanely.

Asked to address their government, one soldier said, “We don’t want to be at war.”

The separatists have rebuffed the cease-fire proposed by Ukraine’s new president, Petro Poroshenko, in his inaugural speech Saturday.

At a meeting Sunday with an OSCE official and Russian Ambassador Mikhail Zurabov, Poroshenko suggested that a truce should be put into effect quickly.

“We must cease fire this week,” he said. “Each day when people die, when Ukraine pays such a high price, is inadmissible for me.”

OSCE monitors offered a dour assessment, however, noting that officials with the Donetsk People’s Republic see a prisoner exchange, the withdrawal of government troops and political recognition as the only items worth discussing.