President Abdul Fattah al-Sisi's remarks came after the airline said that the Kogalymavia Airbus A-321 crashed over the Sinai peninsula on Saturday due to "external" factors and not technical failure.
"When there is propaganda that it crashed because of ISIS, this is one way to damage the stability and security of Egypt and the image of Egypt," el-Sisi told the BBC in an interview.
He welcomed all those interested in the matter to participate in the investigation into the crash.
An Islamic State affiliate in Sinai has claimed that it brought down the plane which was bound for St Petersburg in Russia from the Red Sea resort of Sharm el-Sheikh.
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A primary analysis of the two black boxes of the Russian plane that crashed last Saturday in the Sinai peninsula showed that the plane was not struck from outside and that the pilot did not make a distress call, sources in the committee investigating the records of the black boxes said yesterday.
Both Egypt and Russia have played down the claim by Egypt's IS branch that it brought down the plane.
Investigators are examining all possible causes as they comb the remote crash site as part of an Egyptian-led probe into the disaster that also involves experts from Russia, Airbus, and Ireland, where the aircraft was registered.
El-Sisi is expected to arrive to the UK tomorrow after receiving an official invitation from the British government.
During his visit, the President will meet Prime Minister David Cameron to discuss strategic issues, including fighting terrorism, democracy in Egypt and economic ties.