Russian rescuers have found the first parts of the Syria-bound military plane that plunged into the Black Sea, as officials said they do not suspect terrorism as the reason for the crash that killed 92 people on board.

The Tu-154 jet, whose passengers included more than 60 members of the internationally-renowned Red Army Choir, was heading to Moscow's military base in Syria when it went down off the resort city of Sochi shortly after take-off Sunday.

Nine Russian reporters were also on board as well as military servicemen and Elizaveta Glinka, a prominent member of President Vladimir Putin's advisory human rights council.

Investigators have yet to confirm the cause of the crash, but officials said that an act of terror was not being considered as a possible explanation, despite the plane and its black boxes still being underwater.

A spokeswoman for the Sochi-based search and rescue branch of the emergency ministry confirmed that parts of the plane had been found underwater.

"The debris is at the depth of 27 metres one mile from shore," spokeswoman Rimma Chernova told AFP.

The Russian military added that divers had retrieved "two elements of the plane's control mechanism."

Rescuers unload fragments and remains from a boat, found at the site of the Tu-154 plane crash near Sochi, Russia, December 25, 2016. (AFP)

Russia's federal security service said it is looking into four suspected causes of the crash, which do not include terrorism.

"No signs or facts pointing to a possible act of terror have been received at this time," Russia's Federal Security Service said in a statement carried by national news agencies.

The probe is focusing on a pilot error, a technical fault, bad fuel and a foreign object in the engine as four main scenarios, it added.

Flags were flown at half-mast on Monday, mourners placed flowers at the airport in Sochi, southern Russia.

More than three thousand people are racing to find the remaining bodies and debris in a massive operation that includes 45 vessels, planes, helicopters, and drones, along with divers and remotely-operated deep-water machines.

Transport Minister Maxim Sokolov said some of the bodies could have already been carried off by the "strong current" to Abkhazia, the separatist region of Georgia, and some of its own rescue workers have joined the search operation.

Along with the first 10 bodies, 86 body fragments were brought to the Russian capital for DNA analysis, defence ministry spokesman Igor Konashenkov said.

He said searchers have finished looking over the on-land territory around the crash site while divers are working over an area with a radius of 500 metres.

The passenger jet went down on Sunday morning minutes after taking off at 5:25 am (0225 GMT) from Sochi's airport, where it had stopped to refuel after flying out from the Chkalovsky military aerodrome in the Moscow region.

Onboard were 64 members of the Alexandrov Ensemble -- the army's official musical group, also known as Red Army Choir -- and their conductor Valery Khalilov.

"The ensemble has been orphaned by a third," said state channel Rossiya.

The choir was set to perform for Russian troops at the Hmeimim airbase, which has been used to launch air strikes in support of Moscow's ally President Bashar al-Assad.

"These people were flying to Syria to support and wish happy holidays to those who are serving their military duty there," Prime Minister Dmitry Medvedev said after opening a government meeting, which held a moment of silence.

Other passengers included military officers, journalists and popular charity worker Yelizaveta Glinka, also known as Doctor Liza, who had been flying with a cargo of medical supplies for a hospital in the coastal city of Latakia.

One of the passengers was the head of the defence ministry's culture department Anton Gubankov, who worked to popularise the armed forces, including by authoring the song Polite People which honoured special forces officers who oversaw the annexation of Crimea.

President Vladimir Putin ordered a national day of mourning on Monday, with state television flashing black and white pictures of the victims across the screen while entertainment programmes were cancelled.

People brought flowers to improvised memorials at the port in central Sochi and the city's airport, as well as to the Moscow headquarters of the Red Army Choir and the office of Fair Aid, the NGO that Glinka headed, which primarily worked with Moscow's homeless.

"I know all of them. I cannot believe it, can't collect myself," said Vladimir Kuznetsov, a former member of the Alexandrov Ensemble who came to pay his respects.

"They knew us all over the world, we went everywhere," he said of the troupe, holding a candle in a plastic cup.