Russia's ruling party headed to a convincing victory in Crimea polls on Monday, with a preliminary count showing it won more than 70 percent in the first local elections since the peninsula's annexation from Ukraine in March.

Crimea's residents joined Russians across the country in voting in local elections on Sunday which saw President Vladimir Putin cement his grip on power.

U.S.-led military exercises began in Ukraine on Monday after a day of deadly fighting between government forces and pro-Russian rebels in the restive east that has piled pressure on a shaky 10-day-old truce.

Local officials said six civilians died during heavy shelling around the rebel stronghold of Donetsk on Sunday, with Kiev accusing the separatists of jeopardizing the truce by intensifying attacks against government positions.

The Ukrainian government accused pro-Russian separatists on Sunday of threatening a tenuous push for peace as booming rounds of heavy artillery fire echoed across the insurgent stronghold of Donetsk.

It said the rebels had been intensifying their attacks on government positions in eastern Ukraine despite a ceasefire backed by Kiev and Moscow nine days ago.

Thousands of Ukrainians congregate every day at the border post of Izvaryne, one of the main crossing points between Russia and the breakaway eastern region of Lugansk, shell-shocked by months of fighting.

On Ukraine's side of the frontier in the Lugansk People's Republic (LPR), as it was christened in May by pro-Russian separatists, a line of cars stretches down a crumbling road leading to the border.

Russia has delivered a second shipment of aid to rebel-controlled Ukraine, sending trucks carrying 2,000 tons of goods unaccompanied across the border, national television said on Saturday.

"The second humanitarian mission brought 2,000 tons of aid to Donbass," said a news ticker on Russian state-owned channel Rossiya 24, referring to the rebel-held region of east Ukraine.

The United States is using the Ukraine crisis to cut economic ties between the EU and Russia and force Europe to pay more for its gas, Russian Foreign Minister Sergei Lavrov said Saturday.

"The U.S. is trying to use the crisis in Ukraine to break economic ties between the EU and Russia and force Europe to buy U.S. gas at much higher prices," Lavrov said in a ministry statement of his interview with Russia's Center TV.

The Ukrainian military said Saturday its forces had repelled an insurgent attack on the airport in the eastern separatist stronghold of Donetsk, despite an eight-day ceasefire.

"Many rebels backed by six tanks launched an assault against the airport on Friday which was heroically repelled by the soldiers," the press service for the military operation in eastern Ukraine said.

Ukrainian forces and pro-Kremlin insurgents said Friday they have swapped dozens of prisoners under the terms of a fragile truce aimed at ending the five-month eastern revolt.

Separatist leader Andrei Purgin said 31 guerrillas were swapped overnight for 36 Ukrainian soldiers in a town north of the rebel stronghold of Donetsk.

The U.N.'s World Food Programme announced Friday the launch of its first food aid operation in Ukraine, saying it had begun distributing rations in the country's conflict-torn east.

Dutch prosecutors said Friday they need to know where a missile that may have shot down flight MH17 was fired from in eastern Ukraine before criminal charges could be laid.