The two French companies were identified by Reuters as Deep Ocean Search and Alseamar.
A report by The AP quoted an unnamed senior official who said body remains suggested an explosion had occurred.
Egyptian forensics official says body parts bore marks consistent with an explosion.
In their 30-minute meeting, the two religious heads are reported to have discussed the problems of violence and terrorism.
A senior Egyptian aviation official said there was no unusual movement before the Airbus A320 crashed.
The funeral for Yara Hani Tawfik took place in Cairo as investigators look for answers.
Geologist Richard Osman was on board the EgyptAir flight MS804 that reportedly crashed in the Mediterranean.
Earlier statements said plane debris had been discovered near the Greek island of Karpathos.
During the 'New Kingdom', Egypt ruled northern Sudan, leading to Egyptian and Nubian communities merging.
Egypt's aviation industry has suffered a number of setbacks over the past year.
30 Egyptians, 15 French and 1 Briton among passengers on flight MS804.
Country has become a hub for weapons and munitions smuggling across the region since 2011.
A leading Islamic authority warns against the smartphone app called 'Hurouf'
Protesters see deal with Saudi Arabia on two islands as a sell-out.
Some 60 fire engines battled the worst of the blazes for more than 24 hours before they were finally quelled.
An international conference in Egypt has highlighted need for new tests on King Tut's tomb.
Gunmen stopped a police vehicle before opening fire on the officers south of Cairo.
The Jewish festival of Passover begins on Friday 22 April and lasts until Saturday the following week.
EgyptAir hijacker fears he will be given a death sentence in Cairo and requests asylum in Cyprus.
It is unclear why the Italian government has revoked Hacking Team's licence.
Social media users horrified after European Space Agency reveals River Nile satellite image as blood red.
More research required to say if the Pharaoh's tomb hides secret burial chamber of Queen Nefertiti.