Tactics of the "anti-terrorist operation" in eastern Ukraine must be tailored to avoid civilian casualties, Ukrainian President Petro Poroshenko said Monday.

"There is a need to change the tactics (of the operation), such as to narrow the zone of actions, enhance border protection and do everything to ensure the protection of civilians," Poroshenko said at a meeting with law enforcement agencies.

Fierce fighting and heavy casualties, in the restive Donetsk and Lugansk regions, have been reported since the government forces resumed military operations against insurgents since the start of this month.

According to the presidential press service, Poroshenko said the active phase of the counter-terrorist operation was continuing.

Poroshenko ordered Roman Romanov, head of Ukraine's state-run defense industry group Ukroboronprom, to supply more arms to the government troops engaged in the military operation in Donetsk and Lugansk regions within a week.

"The most important thing the people need now is security," Poroshenko said.

He stressed the servicemen have been responsible for restoring a peaceful life in those regions.

"If power is taken, it is important to not just hoist the flag, but also to defend the state and people (it represents)," Interfax news agency quoted Poroshenko as saying.

Insurgents said on Monday that they had shot down an An-26 military transport plane near the city of Lugansk.

Later in the day, the mayor of Donetsk, currently under control of the self-proclaimed Donetsk People's Republic (DPR), fled the city.

Mayor Oleksandr Lukyanchenko said he has fled the city because of the death threats from the DPR leaders.