Intelligence officials from the United States and Western countries believe that an explosion brought down the plane presumed to carry Wagner group leader Yevgeny Prigozhin and others.
One of the officials told the Associated Press that the explosion was in line with Russian President Vladimir Putin's "long history of trying to silence his critics."
The official was not permitted to comment publicly and did not want to be named.
Russian officials have not officially confirmed the identity of those who died on the private plane.
However, President Putin expressed sympathy on Thursday to the families of those who were reportedly on the plane.
He also spoke of Prigozhin, saying, "He made some serious mistakes in life, but he also achieved necessary results."
Earlier on Wednesday, U.S. President Joe Biden said he did not know what happened, but he said, "I'm not surprised."
He added, "There's not much that happens in Russia that Putin is not behind."
Prigozhin founded the Wagner group.
It is an organization of fighters based in St. Petersburg who offer their services for money and are not officially linked to the Russian military.
The fighters were known to support military leaders in Africa and the Middle East.
They had also been supporting Russian President Vladimir Putin's war in Ukraine.
But Prigozhin criticized Putin and his military leaders and launched what was called a mutiny earlier this year.
On June 23 and 24, he and his soldiers moved against Russia's leaders, shooting down aircraft and started a convoy of military vehicles targeting Moscow.
The anti-Putin move ended when the two men reached a deal that permitted Prigozhin to go to Belarus.
Reports, however, said he was able to move safely and freely between Russia, Belarus and parts of Africa.
He appeared at a meeting between Russia and African nations in St. Petersburg in July.
Many wondered why Prigozhin seemed safe after moving against Putin.
Other opponents of the Russian president had been sickened, killed or imprisoned in the past.
On Wednesday, rescue workers found 10 bodies, which included members of the Wagner group and the airplane crew.
Russian media reports said Prigozhin was on the plane, citing unnamed people.
The lights on the group's main building in St. Petersburg were lit in the shape of a cross overnight.
By Thursday, supporters made a small memorial with red and white flowers and Wagner Group flags.
There was no official statement from Russia's leaders on the crash or its cause.
However, Rosaviatsia, Russia's aviation agency, published a list of those on board and it included Prigozhin.
A reporter from the Reuters news agency went to the place of the crash on Thursday and spoke to people who said they heard a loud sound before seeing the airplane fall to the ground.
One person, Anatoly, said he heard "a metallic bang" and not the kind of noise from a thunderstorm.
Part of the plane's tail and other wreckage were seen on the ground.
Flight information services showed the plane flying normally until it disappeared from radar.
Prigozhin supporters called him "a hero" on messaging services.
They said the flight had either been shot down by a missile or destroyed by a bomb on board.
Those claims have not been verified, and Russian officials say they are investigating the crash.
I'm Jill Robbins.