But up to 1,000 protesters boarded pick-up trucks or motorbikes to make their way there.
There was no initial attempt to stop the convoy but hundreds of security forces had set up a checkpoint in Bangkok's northern suburbs. Some fired warning shots into the air.
The BBC's Rachel Harvey in the Thai capital said the soldier who died appeared to have been shot in a "friendly fire" incident during a lull in the clashes.
Local hospitals said at least 16 people had been injured.
Army spokesman Sansern Kaewkamnerd told Associated Press news agency: "We brought force out to stop them. Society finds it unacceptable to have protesters travelling in a motorcade like this."
The convoy has now reportedly headed back to its central Bangkok base.
One protest leader, Kwanchai Praipanna, said Wednesday's rally had been planned to thank local people for their support.
Our correspondent says the convoy had been going to a northern suburb where earlier in the week protesters had set up a checkpoint to search vehicles for any troops being brought in to reinforce Bangkok.
Thai PM Abhisit Vejjajiva: 'willing to compromise' with protesters
She says that this does not seem to be the start of a major crackdown to evict the protesters from their main camp, although demonstrators still fear an operation is imminent.
Bangkok itself has remained mostly calm since grenade attacks last week in the business district killed one person and injured 80.
On Tuesday protesters blocked the elevated Skytrain line for several hours but it later reopened.
The weeks-long stand-off has hit Thailand hard, forcing major hotels and shops in central Bangkok to shut.
A government attempt to clear protesters from one area on 10 April left 25 people dead and hundreds injured.
The red-shirts, many of whom support ousted leader Thaksin Shinawatra, say Mr Abhisit's government is illegitimate.
On Tuesday Mr Abhisit told the BBC that while he wanted a political solution to the crisis, immediate elections were not the answer.
"There is a clear threat that if we hold elections too soon, with the mood running as high in terms of divisions and in terms of tension, elections would turn violent and they would solve nothing and we could be back into this vicious cycle of demonstrations."
Meanwhile, the Constitutional Court has said it will consider dissolving Mr Abhisit's Democrat Party over the alleged failure to declare donations in the 2005 election campaign. No timeframe was given for a ruling.
Several governments have been thrown out in recent years following rulings instigated by the Electoral Commission.
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