* Fighting on the rise in east Ukraine
* Attempts to restart peace talks have stalled
* (Adds Ukrainian foreign ministry comment)
By Natalia Zinets and Lina Kushch
KIEV, Jan 18 (Reuters) - Ukrainian troops have recaptured almost all the territory of Donetsk airport in eastern Ukraine they had lost to separatists in recent weeks and thousands gathered in Kiev for a state-sponsored peace march.
Sunday's offensive brought fighting close to the industrial city of Donetsk, center of a pro-Russian rebellion, while shelling intensified in other parts of the region known as "Donbass."
With attempts to restart peace talks stalled, pro-Russian rebels have stepped up attacks in the past week and casualties have mounted, including 13 civilians killed in an attack on a passenger bus, which Kiev blamed on the separatists.
Military spokesman Andriy Lysenko said the army's operation had returned battle lines near the airport to the previous status quo and thus not violated the 12-point peace plan agreed with Russia and separatist leaders last September in Minsk.
"We succeeded in almost completely cleansing the territory of the airport, which belongs to the territory of Ukrainian forces as marked by military separation lines," he said.
Another military spokesman said the firing was continuing early on Monday: "There is firing going on in the airport area and also at various parts of the line of separation. The situation has not particularly improved."
Kremlin spokesman Dmitry Peskov said Moscow was concerned by what he called an escalation by Ukrainian forces that did not contribute to peace efforts.
He later said Ukrainian President Petro Poroshenko had rejected a peace plan contained in a letter Russian President Vladimir Putin sent him on Thursday.
"In recent days, Russia has consistently undertaken efforts as an intermediary in regulating the conflict," Peskov said, according to TASS news agency.
It said Putin's letter included a concrete plan for both sides to withdraw heavy artillery.
Russian television channel NTV published the letter on Sunday evening. 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."
In an overnight statement, the Ukrainian Foreign Ministry called on Russia to sign with Ukraine a timetable for implementing the Minsk agreement which included establishing Ukrainian control over the joint border, withdrawal of foreign forces and heavy military equipment from the region.
"We are convinced that this will allow us quickly to cease fire and protect the civilian population from the firing from (separatist) fighters for the past four months," it said.
"Ukraine steadfastly supports all the points of the Minsk agreements and demands that Russia does also," it said.
Elsewhere in the region, the Ukrainian Interior Ministry said two brothers aged seven and 16 had been killed and their eight-year-old sister wounded when a shell struck a house in the government-controlled town of Vuhlehirsk, 60 km (40 miles) from Donetsk.
Spokesman Vyacheslav Abroskin said the shelling had come from the direction of Yenakiieve, controlled by the rebels.
Poroshenko addressed several thousand people in Kiev late Sunday at a peace march in memory of those killed on the passenger bus.
"We will not give away one scrap of Ukrainian land. We will get back the Donbass ... and show that a very important aspect of our victory is our unity," he said.
Rebel leader Alexander Zakharchenko blamed the shelling around Donetsk on the Ukrainian army. "We're talking about Kiev trying to unleash war again," Interfax quoted him as saying.
The ceasefire agreed in Minsk in early September has been regularly violated since the start by both sides, and fighting has flared up again since plans for peace talks last week were abandoned.
In Donetsk, a coal-and-steel city with a pre-war population of almost 1 million, residents reported a sharp upturn in fighting.
The World Health Organization says more than 4,800 people have been killed in the conflict.
Despite what Kiev and the West says is incontrovertible proof, Russia denies its troops are involved or that it is funneling military equipment to the separatists.
With its runways pitted and cratered, Donetsk airport has long since ceased to function.
But its control tower and extensive outbuildings, battered by shelling and gunfire, have taken on symbolic value, with government soldiers and separatists hunting each other, often at close range, in a deadly cat-and-mouse game among the ruins. (Additional reporting by Jason Bush, and Pavel Polityuk, Writing by Alessandra Prentice, Editing by Richard Balmforth and Timothy Heritage)