* Buildings damaged by shelling near heart of Donetsk
* Route of large Russian aid convoy remains in doubt
* Kiev says aid must be cleared at Ukrainian border (Adds new detail on convoy, casualties, Donetsk violence)
By Thomas Grove
DONETSK, Ukraine, Aug 14 (Reuters) - Artillery shells hit close to the centre of Ukraine's separatist-held city of Donetsk for the first time on Thursday, killing at least one person, as a large Russian aid convoy rumbled towards the border.
With Ukrainian government forces tightening the noose on pro-Russian separatists, shelling rocked Donetsk, sending frightened residents rushing for cover, witnesses said.
It was not immediately clear if the artillery was fired by government or rebel forces.
Two shells landed 200 metres (660 feet) from the Park Inn Radisson, one of the city's main hotels, shattering windows. The blasts opened up a yawning hole on the third floor of an apartment block and left a broad crater on the pavement.
Nearby, a body covered by a sheet lay stretched out on the blood-stained ground.
A huge Russian convoy carrying 2,000 tonnes of water, baby food and other humanitarian aid drove through southern Russia towards the frontier, while Kiev repeated it could not enter until Ukrainian authorities had cleared its cargo.
The pro-Western Kiev government says the humanitarian crisis is partly of Moscow's making and has denounced the dispatch of aid as an act of cynicism. It is also fearful that the operation could become a covert military intervention by Moscow to prop up the rebels who appear on the verge of defeat.
Moscow, which denies charges - also voiced by the West - of giving the rebels heavy weapons, has dismissed as "absurd" suggestions it could use the convoy as a cover for invasion.
By Thursday evening, the convoy had stopped near Kamensk-Shakhtinsky and one of the drivers told Reuters it would be heading to the crossing point at Izvarine, which is held by the Ukrainian rebels.
If this were the case, Ukrainian border guards and customs officers would be unable to conduct proper formalities and make the checks they say are needed on the cargo.
"The cargo will all the same have to be looked at by Ukrainian border guards and transferred to representatives of the Red Cross," said military spokesman Andriy Lysenko on Thursday. It was not immediately clear how this could happen.
The caravan of 280 trucks left the Moscow region on Tuesday, looking to take aid to Luhansk region, in eastern Ukraine, where the main city is held by the separatists.
Even if the convoy was to enter Ukraine via Izvarine, it would not be able to get to Luhansk city without encountering government troops at Novosvitlivka, a settlement which Kiev forces took only on Thursday.
"Ukrainian forces have closed the last possibility for road communications between Luhansk and other territories which are controlled by Russian mercenaries in particular Izvarine," Lysenko said.
Relief agencies say people living in Luhansk and in Donetsk, the region's main industrial hub, are facing shortages of water, food and electricity after four-months of conflict in which the United Nations say more than 2,000 people have been killed.
Ukrainian troops have been slowly encircling Donetsk, which had a peace-time population of nearly a million.
Lysenko said a further nine Ukrainian servicemen had been killed in the past 24 hours up to Thursday afternoon. Regional health authorities said 15 people were killed by a shell which hit a public transport depot at Zurges, east of Donetsk, on Wednesday. The dead included three children.
In Donetsk on Thursday, people poured out of their offices into the stairwell of the city's main administration building after loud explosions nearby triggered an evacuation warning.
A short while later, the whistling sound of incoming shells were swiftly followed by at least two further blasts.
Liliya Chalina, 54, lived in the apartment block whose wall was smashed by a projectile. "It came straight into the apartment. Thank God I was not in the kitchen," she said.
"My husband promised me that shells would never hit our house, only large buildings. But look at what has happened."
A woman called Tamara, who showed a deputy's card for the self-proclaimed Donetsk People's Republic, said she believed the separatist fighters had fired the shells. "One of the fighters said they had done it," she said.
A further round of artillery fire hit central Donetsk later in the afternoon. A Reuters witness heard around 10 explosions and saw a residential building and a garage in flames and a row of small shops which had been destroyed by the blasts.
A separatist spokesman said some people had been killed, but was not able to give exact numbers. (Additional reporting by Maxim Shemetov and Dmitry Madorsky, southern Russia; Writing by Richard Balmforth; Editing by Crispian Balmer)