KIEV, Ukraine (AP) — Parts of eastern Ukraine were wracked by fierce fighting Thursday as government troops sought to snatch back territory from separatist rebels, while a Russian aid convoy to the hard-hit city of Luhansk began to make tentative steps toward its destination.

Russia has been trying to send in over 200 trucks carrying what it says is humanitarian aid to help civilians in Luhansk, but Ukraine fears the move is a ploy to aid the pro-Russian separatists. The convoy has been held up at the border for a week in a dispute over the conditions under which Ukraine will let in the Russian trucks.

Ukraine has accused Russia of arming and supporting the separatists since fighting began in mid-April, a charge Russia has denied.

Some Russian aid trucks began the process of clearing customs at the Russian border next to a rebel-held border post in eastern Ukraine, the Ukrainian border guard service said.

Ukrainian troops have made significant advances into rebel-held territory this week in a conflict that has already claimed more than 2,000 lives and forced over 340,000 people to flee their homes. Ukraine celebrates Independence Day on Sunday and reports are rife that the government is aiming to achieve a breakthrough by that date.

Fighting was still reported Thursday in Luhansk, a day after the government said it had captured much of the rebel stronghold 20 kilometers (12 miles) from the Russian border, Andriy Lysenko, spokesman for the Ukrainian National Security Council, told reporters in Kiev.

The city has been under siege for 19 days, lacking basic amenities like running water or electricity. Residents there are struggling to survive, the International Committee of the Red Cross said Thursday following a visit to Luhansk a day earlier.

"People hardly leave their homes for fear of being caught in the middle of ongoing fighting, with intermittent shelling into residential areas placing civilians at risk," the ICRC said in a statement.

The agency said it has taken all necessary preparatory steps for the Russian convoy. It said it was ready to deliver the aid to Luhansk if both Russia and Ukraine agreed on the strictly humanitarian nature of the convoy and all parties in the fighting gave the Red Cross assurances of safe passage.

An Associated Press journalist saw two Red Cross jeeps heading to an unknown destination Thursday in Ukraine after passing through the rebel-held Izvaryne border post. The Ukraine border statement referred to the Russian crossing on the other side of that post.

Rayan Farukshin, spokesman for Southern Customs district of Russia, said Thursday that 16 aid trucks had entered the Russian customs zone on Wednesday that links up with Izvaryne in Ukraine. He said four of the trucks have been successfully checked by the Russian side, while another four were in the process of being checked. After that, the trucks need to get Ukrainian approval.

The Russian Foreign Ministry on Thursday welcomed what it said was an agreement allowing the convoy to proceed to Luhansk and called on both sides in the conflict to declare a cease-fire for the humanitarian operation.

Even without a formal cease-fire, the passage of the convoy through rebel-held areas and the setting up of aid distribution points in Luhansk and elsewhere could halt the government's recent advances.

Meanwhile, five troops were killed and two civilians died in the past 24 hours in rebel-held areas, authorities said. That followed over 50 deaths in the region Wednesday.

Troops were fighting separatists in and around Ilovaysk near the rebel-held city of Donetsk, even though the town is under government control, Lysenko said.

At least two people were killed and an unspecified number wounded Thursday in an artillery strike on a Donetsk suburb, the mayor's office said. Once home to 1 million, the largest city still held by the rebels has seen one-third of its population flee.

Ukrainian troops claimed Thursday to have seized two Russian armored vehicles outside of Luhansk. Photos provided by the defense ministry showed one vehicle and an array of Russian civilian and army IDs.

Moscow denied the reports. A spokesman for Russia's defense ministry told Russian news agencies that the armored vehicle in the photos did not belong to Russia and the documents found in the vehicle had not been used for five years.

Ukraine is also looking for a diplomatic solution to the conflict. President Petro Poroshenko is hosting German Chancellor Angela Merkel on Saturday and is going to Minsk, Belarus, early next week to meet with Russian President Vladimir Putin, EU officials and the leaders of Belarus and Kazakhstan.

During a visit Thursday to the southern city of Mykolaiv, the Ukrainian president said he is seeking to reach a peace deal in Minsk.

"We are going to Minsk to talk about peace," Poroshenko said, quoted by his press office. "The whole world is tired of war."

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Laura Mills and Lynn Berry in Moscow and Frank Jordans in Berlin contributed to this report.