According to Russian media, thousands of people came on Monday to Tsentoroi, the settlement in southeastern Chechnya that is home to Kadyrov's clan, a day after the Moscow-backed leader was killed by a bomb blast.
Mourning ceremonies were to go on for three days, reports said.
Funerals were to be held elsewhere for others killed in the blast, including Khusein Isayev, the head of Chechnya's State Council and Reuters photographer Adlan Khasanov.
The blast ripped through a stadium grandstand in the Chechen capital Grozny on Sunday during a Victory Day parade celebrating the anniversary of the Nazi defeat in the second world war.
Top commander wounded
The Grozny emergency medical centre said 24 people in all were killed and 46 wounded.
Among the wounded was the top Russian military commander in Chechnya, Colonel-General Valery Baranov, who officials said was in a critical condition and had a leg amputated.
Maskhadov has denied killing
There was no claim of responsibility for the blast, but suspicion inevitably fell on Chechen rebels who are fighting both Russian soldiers and Chechen security forces employed by the regional government and Kadyrov's administration.
Chechen separatist leader Aslan Maskhadov denied on Monday involvement in Kadyrov's assassination.
In a statement released on the Chechenpress internet site, Maskhadov said he "condemns all of terrorism".
He said: "We fully understand that death and violence will never solve our problems. The leadership of Chechnya (Maskhadov's team) wants to keep to a real, civilised political dialogue (with Moscow)."
Kadyrov, appointed by Moscow as Chechnya's new leader and later dubiously elected Chechen president, was Maskhadov's arch-foe.
Citing the regional police, reports said five people were detained - all Chechen residents about 25 to 30-years old - but Interfax later quoted the top prosecutor for southern Russia, Sergei Fridinsky, as saying nobody was in custody.
Chechen Prime Minister Sergei Abramov has taken over as acting president of the region, but the killing of Kadyrov - who was the key figure in Putin's efforts to wrest control over Chechnya from the rebels and lend legitimacy to Russia's rule over the region - clouded the future.
News reports said Russian officials pledged a new presidential election would be held in Chechnya within four months, as stipulated in its constitution, but there were calls among pro-Putin Russian politicians for direct presidential rule by the Kremlin.
"This will lead to quite serious changes in the system of rule in republic, because the system that was formed was built in accordance with (Kadyrov's) methods of controlling the situation," said Shamil Beno, a former separatist Chechen official who now works as human rights activist in Moscow.
"This will lead to quite serious changes in the system of rule in republic, because the system that was formed was built in accordance with (Kadyrov's) methods of controlling the situation"
Chechen human rights activist
The bombing - which thwarted the heavy security in place for official ceremonies nationwide - harshly underlined the difficulties Russia faces in controlling the violence in Chechnya despite a massive troop presence.
It was expected to set off a new round of killing between Kadyrov's camp and his enemies who had long pledged to eliminate him.
The explosive was believed to be a land mine, said Sergei Kozhemyaka, a spokesman for the southern Russian branch of the Emergency Situations Ministry.
NTV television quoted an investigator as saying it had been made out of a 152mm artillery shell and detonated with a wire or timer.
It was planted under the seats where Kadyrov and other dignitaries were watching the ceremonies.
The ITAR-Tass news agency reported that the mine was planted under the concrete floor of the VIP podium, and that investigators were trying to identify people who had worked on the three-month renovation of the stadium, which was completed just before the holiday.
Sergei Abramov (L) is the new
Kremlin-imposed Chechen leader
Citing Chechnya's acting chief prosecutor, Vladimir Kravchenko, Russia's First Channel television reported that two unexploded devices were found in the area later.
Kadyrov, a former separatist who broke with other rebels and sided with the Kremlin at the start of the second Russia- Chechen war in 1999, was a top target of the rebels and had survived several assassination attempts.
Previous major attacks in Chechnya have been followed by massive operations to find the perpetrators, with troops and security forces sealing off whole neighbourhoods and towns, conducting house-to-house searches and detaining scores of people.
This attack in particular was expected to increase fear in Chechnya, where Kadyrov's security service, run by his younger son Ramzan, has been accused of being behind civilian disappearances and killings. Both Kadyrovs denied the accusations.
"Justice will take the upper hand and retribution is inevitable," Putin said at the conclusion of Moscow's Victory Day parade on Red Square on Sunday, ITAR-Tass reported.