He told the BBC that it was too early to say what had caused the crash.
The Airbus 321 is thought to have broken up in mid-air over the Sinai peninsula on Saturday, killing all 224 people on board.
On Monday, the airline Kogalymavia blamed “external influence” for the crash.
But the head of Russia’s Federal Aviation Agency, Aleksandr Neradko, told Russian TV that such talk was premature and “not based on any proper facts”.
President Sisi also warned against jumping to conclusions, telling the BBC: “All those interested in the matter are welcome to participate in the investigation.
“When there is propaganda that it crashed because of Isis (IS), this is one way to damage the stability and security of Egypt and the image of Egypt. Believe me, the situation in Sinai – especially in this limited area – is under our full control.”
The US director of national intelligence, James Clapper, said there was no “direct evidence of any terrorist involvement yet” adding: “It’s unlikely, but I wouldn’t rule it out.”
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The Islamic State (IS) affiliate known as Sinai Province issued a written statement and an audio message saying that it brought down the passenger jet.
The group, which pledged allegiance to IS a year ago, is thought to be aiming to take control of the Sinai Peninsula in order to turn it into an Islamist province.
However, experts doubt it possesses the weapons capable of bringing down an airliner.
The Airbus 321 had been carrying 217 passengers, including 25 children, and seven crew members. Most of those on board were Russians.
It crashed 23 minutes after taking off from the Egyptian Red Sea resort of Sharm el-Sheikh en route to the Russian city of St Petersburg.
The plane’s flight recorders have been found and sent for analysis.
Debris was spread across a wide area of Sinai, officials said.
At a news conference in Moscow on Monday, the deputy director of Kogalymavia which owns the Metrojet fleet of aircraft, ruled out a technical fault or pilot error.
“The only [explanation] for the plane to have been destroyed in mid-air can be specific impact, purely mechanical, physical influence on the aircraft,” Alexander Smirnov said.
“There is no such combination of failures of systems which could have led to the plane disintegrating in the air,” he added.
He said the plane lost speed and started descending rapidly, and the crew made no attempt to get in contact and report about the situation on board.
The US broadcaster CBS News reported that a US satellite had detected a “heat flash” over the Sinai at the time the Russian plane crashed.
It said the data was still being analysed and although the flash could have been caused by a bomb, it was also possible that a mechanical failure had caused an explosion in a fuel tank or the engine.
So far, the bodies of more than 140 of those killed in the crash have been flown back to St Petersburg.
A number of bodies have already been identified, Russian media reports say.