Chechen Prime Minister Sergei Abramov has taken over as the new leader of the republic, after the assassination of President Akhmad Kadyrov on Sunday.
Putin appointed Abramov (left) to fill Kadyrov's shoes
The Kremlin-backed president was among those killed in a bomb attack in the capital, Grozny, on Sunday.
Three days of mourning are now underway in Chechnya and Mr Kadyrov is being buried in his home village on Monday.
Russia's President Vladimir Putin vowed revenge for the bombing, which is being blamed on Chechen guerrillas.
Mr Abramov, who was in Moscow at the time of the blast, is reported to be consulting his cabinet about how to respond.
The estimated death toll varies between six and more than 30. About 50 are thought to have been wounded.
Security forces throughout Chechnya have been placed on high alert and Russia's Itar-Tass news agency has reported that five people have already been detained on suspicion of involvement with the attack, according to interior ministry officials.
Mr Kadyrov was fatally wounded when a device exploded during a ceremony marking victory in World War II.
The bombers struck during a Victory Day ceremony
The bomb went off in a VIP seating area of the packed Dynamo stadium in Grozny.
Officials say the bomb was made out of a 152mm artillery shell and detonated with a wire or timer.
Chechnya's acting prosecutor Vladimir Kravcheko said the bomb had been placed inside a concrete part of the stadium which meant it escaped detection in security sweeps.
"Everything points to a well-planned terrorist act, prepared over a long period of time, not just a few days," he said.
There is uncertainty over the fate of the commander of Russian troops in Chechnya, Gen Valery Baranov, who was also in the stadium at the time.
Officials have denied reports that he was killed by the blast and said he was fighting for his life in hospital.
Russian television showed chaotic scenes as panic-stricken spectators ran from the scene and brown smoke rose from the debris of the stand.
One man was seen carrying an injured child to safety, while bursts of gunfire rang out.
Born in Kazakhstan in 1951
Studied Islam and became Chechnya's mufti in 1995
Sacked as mufti in 1999 after falling out with separatist leader Aslan Maskhadov
Appointed as head of pro-Moscow administration by President Putin
The emergency ministry spokesman said a second device had been found following the evacuation of the stadium.
Chechen interior ministry officials quoted by the AFP news agency said at least 32 people had been killed - however other reports put the death toll at six.
Mr Putin, speaking at the end of the Victory Day parade in Moscow, said: "There can be no doubt that retribution is inevitable for those whom we are fighting today. It will be unavoidable for terrorists."
He said Mr Kadyrov's work had proven there was a difference between
"bandits, terrorists and the Chechen people".
Russia has been fighting separatists in Chechnya since the republic first tried to break away in the 1990s.
Moscow has reimposed its rule in Grozny, but rebel attacks have continued, both in Chechnya and elsewhere in Russia.
Mr Kadyrov's assassination has drawn broad international condemnation.
A White House spokesman said Washington resolutely rejected all acts of terrorism, while the European Commission described the blast as a " heinous attack".
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