The aircraft crashed early on Saturday morning in a mountainous area 23 minutes after take-off from the Red Sea resort of Sharm el-Sheikh, one of the most popular destinations for Russian tourists. All 224 on board were killed, making it Russia's deadliest-ever air disaster.
Mr Smirnov said depressurisation of the cabin alone could not have caused a crash as in that case the crew would have tried an emergency landing.
However, Metrojet executives said a video circulated online, in which Isis, the Islamist militant group, appeared to take responsibility for downing the airliner, was believed to be fake.
Airline officials said it was too early to draw conclusions about what caused the crash. Dmitri Peskov, spokesman for Vladimir Putin, Russian president, said no possibility should be excluded.
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Rostrud, Russia's labour watchdog, said its examination of the company's labour and occupational health and safety situation — part of a broader government probe following the crash — showed wage arrears of two months. But TH&C, the holding that owns Metrojet, denied the company was in financial trouble.
"The airline doesn't have financial or economic problems which could negatively impact flight safety, we have no grounds for suggesting that," said Oksana Golovina, a TH&C executive.
Some 144 bodies were brought back overnight on an aircraft of Russia's emergencies ministry to St Petersburg, where grieving relatives and thousands of other residents have been laying flowers at the airport to commemorate the victims.
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Mr Smirnov said the aircraft appeared to break up after reaching a cruising altitude of 31,000 feet. It slowed abruptly before falling.
Aviation safety experts on Monday said there were two theories on what could cause an explosive decompression at cruise altitude.
James Healy-Pratt, head of the aviation department at the legal firm Stewarts Law, said the crash could have been caused by a "botched repair" if there had been inadequate work following previous damage to the aircraft or by an on-board explosion.
Investigators should be able to determine quickly whether the crash was caused by a bomb by checking the wreckage for chemical residue or pitting on the metal.
Experts say investigators will also look at whether the accident was caused by a structural failure due to a previous incident when the Metrojet A321's tail was damaged while landing in Cairo in 2001.
There is a precedent for similar accidents after faulty repairs to tail damage. In August 1985, Japan Airlines Flight 123 crashed into a mountain after a repair to its tail came apart, killing 520 people. The rear pressure bulkhead of the Boeing 747 had been repaired seven years earlier.
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TH&C said the Metrojet aircraft had had the "heaviest form of maintenance check" last year.
Airbus said it was providing full "expertise and support" to the authorities investigating the crash. "But we should also give the experts the time necessary to investigate the debris and the information provided by the black box recording devices," a spokesman said.
A person close to the situation said these appeared to be in very good condition. "We expect them to be read within the next few hours or at most a day. They will very quickly reveal what has happened," the person said. The breakup of an aircraft in midair without some external event was "extremely rare," the person added. Many avenues were being explored, from an external attack to an explosion in the cargo hold or cabin of the aircraft.