Three interior ministry soldiers were injured on Monday when an armoured personnel carrier drove over a mine near the village of Shali, south-eastern Chechnya.
Another soldier died later of his wounds, the Ria-Novosti agency, quoting Russian military headquarters in the northern Caucasus.
An army officer and a soldier were injured by a landmine close to Urus-Martan in the south-west of Chechnya, it said.
The Association for Russian-Chechen Friendship, a non-governmental organisation based in neighbouring Ingushetia, said a 24-year-old man from Avturi, a village near Shali, and his father were arrested by the Russian army after the first explosion.
It identified the man as Shamil Alimsultanov, but did not give his father's name.
Russian death squads
More than 400 people disappeared last year in separatist Chechnya, official figures showed on Monday, but a rights group said the real figure might be four times higher.
Pro-Moscow Chechen officials have complained that scores of people disappear every year, driven away by unidentified uniformed men. They have suggested that Russian forces hunting for separatist fighters may be responsible for many cases.
The Russian military in Chechnya has denied the existence of so-called "death squads", which murder local residents on the slightest suspicion of having separatist links.
Russian "death squads" are
accused of murdering Chechens
"According to our information, 444 residents went missing in Chechnya in 2003," a Chechen Interior ministry spokesman said by telephone. "This is 20% less than in 2002."
He said many of those missing were criminals on the run or had joined rebel gangs.
Chechen separatists have fought Russian rule for more than nine years and abductions and killings have become commonplace in the area. Accurate figures are difficult to establish because of an information blackout in the area.
President Vladimir Putin's, whose more than 70% popularity rating before a March re-election attempt owes much to his tough stance on Chechnya, scrapped the post of his human rights representative in Chechnya last month and entrusted Kremlin-backed president Ahmad Kadyrov with the task.
On Monday, the International Committee of the Red Cross (ICRC) said it still did not know where one of its kidnapped Chechen employees was. Usman Saidaliyev was abducted from his home during the night by unidentified armed men, six months ago.
Chechen women bear the brunt of
the kidnappings and murders
"Since then neither Usman's family nor the ICRC have had any news of his whereabouts," the Red Cross said in a statement.
"This is of deep concern to his family and colleagues."
Russian troops poured into Chechnya in October 1999 in what the Kremlin described as an "anti-terrorist" operation, the second such war there in a decade.
The conflict has since degenerated into brutal guerrilla warfare, with troops, insurgents and civilians killed nearly on a daily basis.
About 5000 Russian soldiers have died, according to official figures. Although there are no official figures for Chechen casualties, some estimate that more than 80,000 have died in the last 10 years.