The soldier and the three officers were on patrol in Grozny's Leninsky district on Saturday evening and had stopped two cars to check the passengers' documents, the Interfax news agency reported on Sunday, quoting Maj-Gen Ilya Shabalkin, a Russian government spokesman in Chechnya.
A passenger in one of the cars gave an officer what appeared to be a fake Interior Ministry identification card, Shabalkin said.
When the officer returned to his car to call headquarters, armed men in one of the cars opened fire, killing the soldier and three officers, he said.
The dead included a Federal Security Service official and two Chechen Interior Ministry officers, Shabalkin told Interfax and the ITAR-Tass news agency.
A search for the men is under way, Shabalkin said, adding that authorities suspect one of the men to be Mashugov, who allegedly works with Chechen separatist leader Shamil Basayev.
Shabalkin also said on Saturday a government reconnaissance patrol clashed with about 20 separatist fighters near the village of Surkhakhi in neighbouring Ingushetia.
Shamil Basayev and his men are
blamed for the unrest
At least three fighters were killed, Shabalkin told Interfax.
He did not specify if the reconnaissance patrol was made up of soldiers or members of one of the country's internal security forces.
Shabalkin said the group left behind military equipment and ammunition.
Russian forces withdrew from Chechnya after a devastating 1994-96 war against separatists that left the region de facto independent, but returned with full military might in September 1999 after Moscow blamed the growing unrest on Chechen separatists.
Chechens have been living in fear since the return of the military, due to extreme security measures and oppressive laws.
In a separate incident, a senior police official was killed in the neighbouring Russian region of Dagestan, authorities said on Sunday.
Two armed men on Saturday night fired on Magomed Gadzhimagomedov, who headed a regional branch of the Interior Ministry's criminal investigation division, outside the entrance to his home in Buinaksk, said Abdul Musayev, a spokesman for Dagestan's Interior Ministry.
Chechen residents say they are
harrassed by Russian troops
Gadzhimagomedov, 48, was returning home from his office in Buinaksk, about 30km southwest of the regional capital, Makhachkala, Musayev said.
He had worked for the police department for 20 years.
Dagestan, an ethnically diverse region that borders Chechnya, has been plagued by violence including bombings and shootings, many of which have been blamed on separatists.
Police and Russian soldiers have become targets in the region due to what residents say is harassment, interrogation and at times, severe torture of alleged suspects.