News reports said a bodyguard was killed when a mine struck a motorcade carrying the pro-Moscow acting president, Sergei Abramov, through the devastated regional capital, Grozny.
Abramov, who took over after President Ahmad Kadyrov was killed by a bomb on 9 May, was travelling at high speed in an armoured car and escaped injury.
His convoy was returning from an inspection of construction sites of buildings shattered in Russia's second post-Soviet attempt to crush separatism, launched in 1999.
Interfax said two other members of Abramov's staff were hurt.
"I am alive. Everything is all right," Abramov told First Channel television about 90 minutes after the blast.
A former prime minister of Chechnya, 32-year-old Abramov was thrust into the top job when Kadyrov was killed in a bomb attack during public celebrations.
Elections for a new president are to be held on 29 August, but Abramov is not in the running.
Agencies also quoted local officials as saying Chechnya's elite security force lost 18 fighters in their heaviest fighting in a year with rebels in a village south of Grozny.
The upsurge of violence showed that although Chechen guerrillas cannot mount prolonged large-scale operations against Russian forces, they can still carry out effective hit-and-run attacks on specific targets.
In reports on the overnight fighting at Avtury about 35km south of Grozny, Kadyrov's son, Ramzan, said 18 members of the force he heads had been killed.
Eighteen elite soldiers were killed
in clashes with rebels
"The battle lasted from 11pm on Monday until Tuesday morning," Kadyrov said.
"We suffered the heaviest losses among Chechen security forces in a single operation in a year," Itar-Tass news agency quoted Kadyrov as saying.
A Chechen Interior Ministry spokesman confirmed the clash, but said only that 24 rebels had been killed. NTV television said six people had died altogether.
Hit and run
It is nearly five years since Russian troops poured back into Chechnya for the second time to end effective independence won in a 1994-96 war with Moscow.
Russian troops and pro-Moscow Chechen forces suffer weekly casualties in hit-and-run attacks and raids on bases of splintered guerrilla groups.
Ahmad Kadyrov was killed in a
Ahmad Kadyrov ruled Chechnya with a firm hand, building a power base by negotiating the surrender of some rebels.
The Kremlin has signalled it is backing Alu Alkhanov, the region's Interior Minister to succeed him after the August election.
Troops under his command vie for control of Chechnya with Ramzan Kadyrov's security forces.
With recent violence hitting Russian-supported Chechens and Russian military, the 200-year struggle seems to have no end in sight.
Located in the mountainous region in the Caucasus range and inhabited by a mainly Muslim population with a fiercely independent spirit, Chechnya has seen anti-Russian fighting since the late 1700s.
During the second world war, Soviet leader Josef Stalin distrusted the Chechens and deported them en masse to Central Asia in 1944.
They were allowed to return in 1957 under premier Nikita Khrushchev.
After Dzhokhar Dudayev declared independence at the end of Soviet rule, President Boris Yeltsin sent in troops in December 1994 and Russia became mired in war.
Stiff rebel resistance led to a truce being signed and Moscow withdrew its forces but returned shortly before Vladimir Putin became Russia's president in 1999.