Fighting in eastern Ukraine intensified on Tuesday ahead of much-anticipated peace talks, with both sides claiming significant advances and the government accusing the rebels of shelling a town far behind the front lines.

The intense fighting, which the United Nations says has killed more than 5,300 people since April, comes ahead of a crucial summit involving Western leaders on Wednesday, as well as peace talks later Tuesday.

Ukrainian President Petro Poroshenko told parliament that Russian-backed rebels launched an artillery strike on the town of Kramatorsk, which is more than 30 miles away from the front line. Poroshenko said the first round of rocket fire hit the headquarters of the Ukrainian command in eastern Ukraine and the second landed in a residential area.

The government-controlled Donetsk regional administration said three people were killed and 15 injured in the artillery strike.

Kramatorsk was the site of major fighting until July when the rebel separatists retreated from it.

Local website Donetskiye Novosti posted photos from the scene, showing an artillery shell stuck in the ground next to a residential building and two bodies lying nearby.

The volunteer Azov battalion, loyal to Kiev, said on social media on Tuesday that it captured several villages northeast of the strategic port of Mariupol, pushing the rebels closer to the border with Russia. However, rebel military spokesman Eduard Basurin said in a televised news conference that the rebels have not retreated.

The Azov said rebels shelled the village of Kominternove, east of Mariupol, causing unspecified civilian casualties. An Associated Press reporter at a government checkpoint between there and government-controlled Mariupol was told of ongoing fighting several miles away. Two ambulances and four pickup trucks carrying Ukrainian troops were seen coming from the direction of Kominternove toward Mariupol.

The rebels reported advances, too. Basurin said late Monday that they have surrounded the railway hub of Debaltseve, the focus of fierce fighting in the past weeks, cutting it off from a major highway. Al Jazeera's Charles Stratford, reporting from the nearby town of Yanovka, spoke to a rebel commander who supported Basurin's claims.

"We have just spoken to a rebel separatist commander who tells us Debaltseve is completely surrounded by separatists. As he understands it the separatists are not in the town, the Ukrainian military are still inside," Stratford said. "The military are denying this, saying there are ongoing battles on the main supply route out of the city. We were on that supply route yesterday and the Ukrainian military we saw were in a state of disarray.”

At least seven Ukrainian troops were killed overnight in the east, Ukrainian military spokesman Anatoliy Matyukhin said on Tuesday. In the rebel stronghold of Donetsk, which comes under constant shelling, two civilians were killed and 12 injured.

The fierce fighting and a mounting death toll comes amid renewed efforts to work out a peaceful solution to a conflict that has displaced at least 1 million people and left the Ukrainian economy in ruins.

Representatives of Ukraine, Russia, the rebels and the Organization for Security and Cooperation in Europe are meeting for long-anticipated talks later on Tuesday to lay the groundwork for a meeting on Wednesday between the leaders of Russia, Ukraine, Germany and France.

The Kremlin on Tuesday warned the West against sending weapons to Ukraine or putting pressure on Russia.

Russian President Vladimir Putin's spokesman, Dmitry Peskov, told the Russian News Service radio station on Tuesday that any talk about imposing new sanctions on Russia or arming the Ukraine government would destabilize the situation in Ukraine.

In Washington on Monday, President Barack Obama and German Chancellor Angela Merkel rallied behind efforts to reach a long-shot diplomatic resolution to the conflict, but they offered no clear path for how the West would proceed if talks this week fail. Merkel staunchly opposed arming Ukraine's beleaguered military while Obama dangled the prospect that the U.S. could for the first time send weapons to Ukraine.

Al Jazeera and The Associated Press