* Rebels shoot down Ukrainian army plane in Slaviansk
* Ukraine says member of special forces killed in a clash
* More people fleeing eastern regions as fighting continues
* Poroshenko to be sworn in as president on Saturday (Recasts with plane shot down, adds families fleeing, changes dateline)
By Thomas Grove and Alissa de Carbonnel
DONETSK/LUHANSK, Ukraine, June 6 (Reuters) - Pro-Russian separatists shot down a Ukrainian army plane as fighting raged in the eastern town of Slaviansk on Friday, a day before the inauguration of pro-European billionaire businessman Petro Poroshenko as Ukraine's president.
Slaviansk has been at the heart of a two-month insurgency in the Russian-speaking east of Ukraine by rebels opposed to the overthrow of a Moscow-leaning president and the formation in Kiev of a pro-Western government.
Separatists operating from the grounds of a church in Slaviansk also killed a member of the Ukrainian interior ministry's special forces and seriously wounded two others in a mortar attack on Friday, the ministry said.
The self-appointed mayor of the city, Vyacheslav Ponomaryov, said an Antonov An-30 intelligence plane had been shot down.
"The airplane was hit in the centre of the city. It happened in front of my own eyes. It was a wonderful sight. The residents who saw it applauded," Ponomaryov told Reuters by telephone.
A spokesman for Ukraine's "Anti-terrorist operation" or ATO, later confirmed a plane had been shot down but said it was an An-26 transportation plane carrying humanitarian aid.
The Ukrainian army and defence ministry were not available to comment on the reports. A YouTube video purporting to be of the An-30 and posted on several local news websites showed a plane clearly heading downwards in an irregular manner.
A photographer in Slaviansk, a city of 130,000 people in the province of Donetsk bordering Russia, said she saw the plane, visibly on fire, slowly descending but did not see it crash.
Residents said the sounds of shelling reverberated around the city on Friday. One separatist in Slaviansk told Reuters there had been shooting in the city centre and that there were casualties, although he did not know how many.
Resident Larissa Akincheva said she stayed away from her work as a store clerk due to the heavy shelling.
"Today I didn't go out at all. I hear the explosions, the shelling. They have been firing all day," Akincheva, 50, said by telephone. "You could hear the planes circling overhead, I don't know if they were scouting or what."
Fighting in the regions of Donetsk and Luhansk has intensified since Poroshenko's victory in the presidential election on May 25. The vote was called after the flight of Viktor Yanukovich in February after months of protests in Kiev.
Poroshenko was in France on Friday for ceremonies marking the 70th anniversary of the Allied D-Day landings of World War Two. There, he met world leaders including Russia's Vladimir Putin, who denies charges by Kiev and the West that Moscow is actively supporting the separatists.
There are signs that an increasing number of families are fleeing the violence in the two regions. With the Donetsk airport still closed after heavy fighting almost two weeks ago, people are taking to their cars and driving to the border.
At a small border crossing in Izvaryne about 70 kilometres southeast of Luhansk, a queue of more than forty cars inched along the hot sun-warmed tarmac toward the Russian border.
"It is the only open border post on the southern part of Luhansk," a young border guard said, without giving his name because he was not authorised to speak to media. He said some four other nearby border posts were closed.
"We decided to leave after the air strike on Luhansk and the clashes around the Mirny border control - that's where we live," said Elena, 43, who was heading to Crimea on the Black Sea with a daughter and a 12-month-old grandchild. She said mortars had been falling close to her home for 24 hours.
"We are leaving because we cannot live with these Ukrainian killers," she said.
But not all border posts are safe - late on Thursday, Ukrainian forces fended off an attack on a post some 95 km (60 miles) to the east of Donetsk using air strikes, the border service said in an English-language statement.
It said five Ukrainian personnel were wounded and according to "preliminary information", 15 separatists had been killed.
"They drove around us in circles shooting for about four or five hours," said Vadim, an officer at the border post wearing a camouflage T-shirt and cap with the Ukrainian trident on it.
"They didn't ask us to give up, lay down our weapons or make any attempt to communicate at all. They just shot," he said, adding he hoped reinforcements would arrive "soon". He said there were 100-150 attackers.
The rebels' two armoured personnel carriers, one of which had the name of the separatist formation "Battalion Vostok" painted on it, and a military transport vehicle covered in bullet holes stood abandoned at the checkpoint.
A spokesman for the Vostok Battalion was unavailable for comment. A spokeswoman for the separatists said she had no information about losses from the rebel side in this incident. (Additional reporting by Alexander Reshetnikov in Donetsk and Richard Balmforth and Pavel Polityuk in Kiev; Writing by Sabina Zawadzki; Editing by Gareth Jones)