The clash left nine people injured, two of them seriously.
The question was raised by UDD chair Tida Thawornseth at a press conference at the Lat Phrao Imperial Department Store.
Ms Tida showed to the press images and video clips of the Lak Si clash. She said the evidence showed groups of two to three men, each clad in black, opening fire at the red shirts.
In each team, there was a shooter and one or two others pinpointing the targets, she said. She denied a suggestion by an appointed senator made to foreign reporters that it was the red shirts opening fire at each other, but did not name the senator.
Ms Tida said from the clips the men in black wore a green arm-band, similar to the one issued by the Thai Journalists Association, and were clearly trying to disguise themselves as reporters. In fact, they were PDRC men, she added.
"In the pictures, soldiers sat watching what was happening, doing nothing. Was it because they were all soldiers? The way they dressed and their equipment were the same. All the firing was from the PDRC's side. Our brothers and sisters were not armed. They were villagers from the Thung Song Hong housing estate, mostly women," she said.
Ms Tida said the armed men were suspected to be regular soldiers or people used to operating in the jungle.
Yossawaris Chuklom, or Jeng Dokchik, a UDD core member, demanded Mr Suthep answer whether the armed men at the Lak Si intersection were soldiers supporting the PDRC, saying they looked like they had undergone military training.
He also asked Gen Prayuth to reply to the same question.
None of the red shirts at Lak Si were armed and it was they who were attacked in a one-sided engagement, Mr Yossawaris said.