Donetsk (Ukraine) (AFP) - Fierce gunbattles erupted around the Ukrainian rebel stronghold of Donetsk on Wednesday, with two civilians killed just a day after lawmakers in Kiev held out an offer of self-rule to the pro-Russian separatists.

Heavy shelling has been reported around the flashpoint eastern industrial hub almost daily despite the warring sides signing up to a ceasefire deal almost two weeks ago.

Donetsk city hall said two civilians were killed near a market that lies just a few kilometres (miles) away from the battleground at the airport and was left in ruins by shelling earlier this week.

"A man died on the third floor," said 52-year-old businessman Alexander Dudnik as he recounted how a rocket slammed into a building in the working-class Kievsky district.

"He wasn't able to walk. Unfortunately he didn't stand a chance of surviving, because the flames were so big that nobody could rescue him as he burned inside."

Pro-Moscow rebels have so far given Kiev's apparent olive branch a cautious welcome but also defiantly insisted it would not stop their fight for full independence as part of "Novorossiya" ("New Russia").

Lawmakers unanimously approved the "special status" law just moments before they ratified a landmark EU pact that steers Ukraine decisively away from Russia's sphere of influence.

And Moscow, virulently opposed to Ukraine's pro-Western shift, signalled it had no intention of backing down in the most serious standoff with the West since the Cold War.

It announced plans Tuesday to send more troops to Crimea, which it invaded and swiftly annexed in March, in apparent retaliation for US-led war games under way in western Ukraine.

The self-rule legislation and an amnesty law for fighters was drawn up as part of a peace plan signed by both Kiev and Moscow that is seen as the most significant push to end the bloody five-month conflict in Ukraine's rustbelt.

Almost 2,900 people have been killed and at least 600,000 forced from their homes across the war-battered east, according to UN figures.

- 'Stop people dying' -

And since the truce, around 30 civilians and Ukrainian servicemen have been killed, mostly around Donetsk.

Andrei Purgin, deputy prime minister of the self-proclaimed Donetsk People's Republic, said the rebels would study the legislation, describing it as a "positive signal because it marks Kiev's return to reality".

But he also said bluntly that Donbass "no longer has anything to do with Ukraine".

The "special status" legislation gives three years of limited self-rule to the separatist regions of both Donetsk and Lugansk and calls for local polls in December.

It also guarantees the right for Russian to be used in all state institutions -- a particularly sensitive issue in the mainly Russophone regions collectively known as Donbass.

Another law grants amnesty to fighters on both sides, although rights groups have alleged abuses that could be considered war crimes.

- 'Blueprint for transformation' -

Washington said the legislation underscored Kiev's "continuing commitment to resolve the ongoing conflict in eastern Ukraine peacefully."

The European and Ukrainian parliaments held simultaneous votes on Tuesday to ratify a historic political and economic pact whose rejection by the former government last year triggered the current crisis.

Poroshenko said the adoption of the association agreement was Ukraine's first step towards membership of the 28-nation bloc.

"Tell me, who will now dare to shut Ukraine's doors to Europe?" said Poroshenko, who is heading to Washington for talks with US President Barack Obama on Thursday.

EU leaders hailed it as a "blueprint for Ukraine's transformation into a modern and prosperous European democracy".

US State Department deputy spokeswoman Marie Harf said Ukraine had made history "in the face of great challenges".

But the occasion was muted by a decision to delay until 2016 the implementation of a free trade deal, an apparent concession to the Kremlin.

The rejection of the broad EU pact by Kremlin-backed president Viktor Yanukovych in November set off the bloody chain of events that led to his ouster in February, Russia's subsequent seizure of Crimea and the unleashing of the revolt in the east.

Moscow's denials of involvement have not spared it from waves of punishing Western sanctions that have left President Vladimir Putin more isolated than at any stage of his 15-year rule.

Russia further unnerved its neighbours with the announcement it plans to boost troop numbers in Crimea because of the "worsening" crisis in Ukraine and the buildup of foreign troops on its border.

The United States and 14 other countries are staging military drills in western Ukraine and NATO earlier this month unveiled plans to boost its forces in eastern Europe in response to Russia's "aggression".