A French-led search team on Saturday located and collected the second "black box" flight recorder, a day after they had salvaged the first flight recorder.
The French navy had said the second box lay at about 800 metres, but another source close to the salvage operation said the box which records cockpit conversations, was found at a depth of more than 1000 metres.
The recorders are to be sent to Cairo, officials said on Saturday.
Search and rescue experts detected a weak signal from the second flight recorder four days after the plane, carrying 133 French tourists and 15 other people, plunged into the sea minutes after take-off from Sharm al-Shaikh on 3 January.
In Cairo, Egyptian Civil Aviation Minister Ahmad Muhammad Shafiq Zaki told reporters Egypt had the technical means to download and analyse the data from the flight recorder, while personnel from the US plane manufacturer Boeing would take part in the investigation as observers.
If the Egyptians need any help from France, they will ask for it "without embarrassment", the minister added.
Egypt has asserted its sovereign right to take the lead in the investigation and has defended its air safety record against allegations that Switzerland banned the operating company, Flash Airlines, from its air space because of safety violations.
French marines assisted Egypt in
locating the plane's recorders
Zaki said: "If it turns out there was a flaw in the plane, we will announce that straight away without any embarrassment."
He said the Swiss ambassador in Cairo had admitted to him that a Swiss official made a mistake when she told reporters that Switzerland had taken steps against the airline.
The ambassador, Raimund Kunz, told Reuters he had told the minister he personally felt it was "not the best moment" to make such a statement so soon after the crash.
"But I could not admit that the Swiss authorities made a mistake," the ambassador added.
Shakir Qilada, the head of the Egyptian inquiry into the crash, took possession of the first recorder at the commercial port of Sharm al-Shaikh after the French navy-led search team
retrieved it late on Friday night.
The "black box", still wet, is in fact orange with the words "flight recorder. do not open" written on its side.
"The box will now be moved to Cairo in a private plane. It will be taken to the laboratories of the civil aviation ministry where it will be analysed," Qilada told reporters at the port.
"If it turns out there was a flaw in the plane, we will announce that straight away without any embarrassment."
Ahmad Muhammad Shafiq Zaki,
Civil Aviation Minister
Qilada had said before the pinpointing of the second box that its evidence would be very valuable.
"If we find the second box we will get a much better picture of what happened," he said.
The first box lay at a depth of about 1000 metres said the head of the Egyptian navy in Sharm al-Shaikh, Tariq al-Gamal.
The search team used a remotely controlled robot on loan from France Telecom to retrieve the flight recorders and have been working 24 hours a day since Tuesday with the robot.
France has vowed to do all it can to find out why the plane crashed.
France says there is no reason to suspect an attack and gives little credence to a previously unknown Islamic group's claim to have brought down the plane shortly after take-off.