Ukrainian President Petro Poroshenko says Kyiv will reassert control over the country's eastern region, where fighting has intensified in recent days between government troops and pro-Russian separatist rebels.

Poroshenko told a peace rally, the Unity March, in central Kyiv on January 18 that Ukraine would not "give up an inch" of its land to the separatists.

Several thousand people gathered at the Independence Square, known as the Maidan, the scene of antigovernment protests that ousted former President Viktor Yanukovych.

People were carrying Ukrainian flags and banners that read "Je suis Volnovakha" in memory of the victims of a recent rocket attack on a commuter bus near the eastern town of Volnovakha.

The January 13 attack killed 12 people in the bloodiest incident in restive eastern Ukraine for months. Kyiv blamed pro-Russian separatists for the shelling, a charge denied by the rebels.

A minute of silence was observed during the rally in memory of all Ukrainian victims of the ongoing conflict in the east.

There were similar rallies in other cities in Ukraine.

In Moscow, Russian President Vladimir Putin's spokesman claimed that Poroshenko rejected a "concrete" peace plan proposed by Putin.

Dmitry Peskov said on January 18 that Putin had sent a letter to Poroshenko late on January 15 proposing a cease-fire by both government forces and separatist rebels in eastern Ukraine, as well as the withdrawal of heavy artillery by both sides.

He claimed Poroshenko had rejected the plan and did not make a counter-offer.

A copy of the letter was published by the Russian television channel NTV. In it, Putin proposed "urgent measures for the cessation of mutual shelling, and also the rapid withdrawal by the sides in the conflict of means of destruction with a caliber higher than 100 mm."

Peskov also said the Kremlin was concerned over "the escalation of hostilities."

Earlier, military spokesman Andriy Lysenko said Ukrainian troops had launched a "mass operation" and retook almost all the territory of Donetsk airport lost to separatists in recent weeks.

"We succeeded in almost completely cleaning the territory of the airport, which belongs to the territory of Ukrainian forces as marked by military separation lines," Lysenko said in a televised briefing on January 18.

The army's offensive at the airport appeared to have brought the fighting to the city of Donetsk itself.

Local residents reported intensified shelling, including from residential areas in central parts of Donetsk, a key separatist stronghold.

Four Ukrainian soldiers have been killed and 32 injured in the past 24 hours, Lysenko said.

The office of the General Staff said separately that three troops had been killed at the airport alone.

With its heavily damaged runways and buildings, the airport no longer functions but has taken on symbolic value for both sides.

The army's offensive at the airport brought the fighting close to the city of Donetsk itself.

Local residents said there had been intense fighting, including in residential areas in central parts of Donetsk, a key separatist stronghold. Several civilians, including children, were reported to have been killed.

Donetsk officials reported "massive damage to housing stock, infrastructure, and communications of the city."

The leader of the self-proclaimed Donetsk People's Republic accused Kyiv of attempting to wage a "new war."

Currently, residential districts in Donetsk and Luhansk "are under intense fire," Aleksandr Zakharchenko was quoted as saying by Interfax on January 18.

The OSCE issued a press release late on January 18 in which its chairperson in office, Serbia's Foreign Minister Ivica Dacic, strongly condemned the latest surge in violence.

Dacic said, "I urge all sides involved in the conflict to immediately invest their efforts in deescalating tensions, to respect the cease-fire, and to proactively engage with the OSCE on achieving full implementation of the Minsk documents."

More than 4,700 people have been killed and many more civilians have been displaced since the conflict in eastern Ukraine began last April.

Ukraine says some 8,500 Russian troops are helping the rebels.

Moscow denies the claim but says Russian "volunteers" are aiding the rebels.

With reporting by AP, Reuters, Interfax, TASS, BBC, and unian.net