A report that senior leader Deng Xiaoping had died added to the chaos. The report, from Taiwan, was denied by the government.
Ming Pao, a Hong Kong newspaper, said a young guard shot conservative Premier Li Peng in the thigh but the wounds were not serious. It said the guard was shot to death immediately.
Chinese sources said they heard the man shot Li because one of his relatives was killed by soldiers in Tiananmen Square, focus of the student protest for democracy.
Zhao Ziyang, the moderate Communist Party chief, was stripped of his post late last month in a confrontation with Li, President Yang Shangkun and Deng, the conservatives who ordered the army action.
Most of the soldiers involved were from the 27th Army, which is based in Hebei province and apparently is led by members of Yang's family. The 27th, which fought China's brief 1979 war with Vietnam, invaded the city Saturday night and rolled into Tiananmen Square, killing hundreds on its way.
On Tuesday afternoon, witnesses said the 27th Army fought with soldiers from Shanxi province's 28th Army, believed loyal to Zhao. There were no reports of casualties.
The brief exchange, including several rounds from a tank cannon, occurred just south of the Military Museum in western Beijing. It followed unconfirmed reports of soldiers fighting soldiers in the western and southeastern parts of the city Monday and earlier.
Hundreds of citizens flocked to the bridge at Muxudi, also in the west, to welcome soldiers yesterday evening who said they were from the 38th Army, based in Beijing.
"Exterminate the 27th Army! Avenge blood with blood!" people in the crowd chanted as they handed buns, eggs and cigarettes to the soldiers.
The 38th Army is said to have opposed the martial law crackdown and refused to fire on civilians. A soldier at Muxudi told The Associated Press soldiers of the 27th fired on his comrades.