Mr Chuvit said he was at a congee stall opposite the Labour Ministry, where many anti-government protest leaders were present, when the incidents occurred on Thursday in Din Daeng district.
The sounds of gunshots did not come from the area where police officers were standing, he wrote on his Facebook page.
The former massage parlour tycoon turned politician said he had given his account of events to Police Region 4 chief Anuchai Lekbamrung.
According to Mr Chuvit, gunshots were being fired at the police even as medics were attending to a critically injured officer who later succumbed to a gunshot wound to the chest.
The fghting broke out between police and anti-government protesters when the latter attempted to disrupt the drawing of numbers for political parties in the Feb 2 election.
Police used tear gas and rubber bullets during the subsequent clashes in which 153 people were injured and two people, an officer and a civilian, were killed.