The Airbus A320 had vanished 10 miles after it entered Egyptian airspace at the border of the flight information region (FIR) between Athens and Egypt, around 30-40 miles north of the Egyptian coast.
An Egyptian Foreign Ministry says that it will work closely with France to investigate what caused the plane to "fall.
EgyptAir Flight 804 was lost from radar at 2:45AM local time when it was flying at 37,000 feet, the airline said.
European air traffic network manager Eurocontrol said that there were no weather issues at the time in the vicinity of the area where the EgyptAir flight went missing.
Egyptian armed forces were searching for the plane, which was carrying 56 passengers, including one child and two babies, and 10 crew. There were 30 Egyptian naitonals, 15 French nationals, and 11 people from 10 other countries on the flight
The company has announced that Egyptian authorities have detected a signal from the plane's emergency transponder. However, Egyptian Authorities denied this.
The pilot had clocked up 6,275 hours of flying experience, including 2,101 hours on the A320, while the first officer had 2,766 hours, the airline said.
Meanwhile, EgyptAir has opened up a crisis center, and is hosting the passengers' families near to Cairo Airport and is providing doctors, translators and other services to the passengers' family members.
Airbus is aware of the disappearance, but "we have no official information at this stage of the certitude of an accident," the company's spokesman Jacques Rocca said.
Ahmed Abdel, the vice-chairman of EgyptAir holding company says there was no distress call from the plane. He also said that there was no special cargo on the flight, and no notification was made to the captain of dangerous goods on board.
Egyptian Prime Minister Sharif Ismail said in a press conference that "it is still too early to say what exactly happened to the plane," and said that nothing, including terrorism, can be ruled out as a cause of the plane's disappearance.
A Greek frigate searching for the missing aircraft discovered two large plastic floating objects in the sea 230 miles south of the island of Crete, Greek defence sources said.
The two objects appeared to be pieces of plastic in white and red. They were spotted close to the area where a transponder signal was emitted earlier, the sources said.
'Nothing is ruled out'
France is ruling nothing out as to why an EgyptAir plane went missing after leaving Paris for Cairo, Prime Minister Manuel Valls said on Thursday.
As he spoke on RTL radio, an official at President Francois Hollande's office said the French leader had just spoken to his Egyptian counterpart and that both sides would cooperate closely on the case.
"We are in close contact with the Egyptian authorities, both civil and military. The Egyptian authorities have already sent air reconnaissance teams to the site, and France is ready to help with the search if the Egyptian authorities ask, of course," Valls told RTL radio.
"At this stage, no theory can be ruled out regarding the causes of the disappearance," Valls said, adding that available information suggested several French citizens were on the flight.
Meanwhile, Greece joined the search and rescue operation for the EgyptAir flight with two aircraft, one C-130 and one early warning aircraft, officials at the Hellenic National Defense General Staff said. They said one frigate was also heading to the area, and helicopters are on standby on the southern island of Karpathos for potential rescue or recovery operations.
The Greek Civil Aviation Chief reported that Greek air traffic controllers spoke to the pilot over the island of Kea, and that the pilot didn't report any problems. He continued, saying that the EgyptAir flight disappeared from radars two minutes after entering Egyptian airspace.
France also plans to send boats and planes to help search for an EgyptAir aircraft, Foreign Minister Jean-Marc Ayrault said.
"Everything must be done to find the plane, that's why we're in contact with the Egyptian authorities...we are mobilising and ready to send our military means, planes and boats, to search for this plane," Ayrault told reporters after a ministerial meeting with French President Francois Hollande.
Meanwhile, the head of Russia's FSB security service Alexander Bortnikov said that the crash of the EgyptAir jet was "in all likelihood" caused by a terrorist act, the RIA news agency quoted him as saying.
Additionally, Egypt's aviation minister said that a terrorist attack was more likely to have taken down the missing EgyptAir aircraft early Thursday morning than a technical failure.
There were no known security concerns about passengers aboard the missing plane but further checks are underway, he told a news conference.
The minister said however that it was still too early to draw any conclusions as to the cause of the plane's disappearance.
Relatives of passengers on a vanished EgyptAir flight have started arriving at Charles de Gaulle Airport outside Paris, where their loved ones boarded the aircraft. The French government is setting up a crisis center for relatives at the airport.
With its ancient archeological sites and Red Sea resorts, Egypt is a popular destination for Western tourists. But the industry was badly hit following the downing of a Russian jet last year, the ongoing Islamist insurgency and a string of bomb attacks in the country.
An Airbus A321 operated by Russia's Metrojet crashed in the Sinai on Oct. 31, 2015, killing all 224 people on board. Russia and Western governments have said the plane was likely brought down by a bomb, and the Islamic State militant group said it had smuggled an explosive device on board.
Reuters reported in January that an EgyptAir mechanic, whose cousin joined Islamic State in Syria, is suspected of planting the bomb, according to sources familiar with the matter.
In March, an EgyptAir plane flying from Alexandria to Cairo was hijacked and forced to land in Cyprus by a man with what authorities said was a fake suicide belt. He was arrested after giving himself up.
EgyptAir has a fleet of 57 Airbus and Boeing jets, including 15 of the Airbus A320 family of aircraft, according to airfleets.com.
The last fatal incident involving an EgyptAir aircraft was in May 2002, when a Boeing 737 crashed into a hill while on approach to Tunis-Carthage International Airport, killing 14 people.
In October 1999, the first officer of a Boeing 767 deliberately crashed the plane into the Atlantic Ocean about 60 miles south of Nantucket Island, Massachusetts, killing all 217 people on board.