The project was discussed during talks in Jerusalem between Peres and visiting Jordanian Foreign Minister Hani Fawzi al-Mulki, the most senior Amman official to hold talks in Israel in nearly four years.
"Mr Peres and Mr al-Mulki agreed to cooperate on moving forward work on building a canal between the Red Sea and the Dead Sea to prevent an ecological catastrophe," a statement from Peres's office said.
Tourism and water desalination were also discussed in the meeting, along with security cooperation and efforts towards reviving peace talks with the Palestinians, it added.
Al-Mulki, who on Saturday visited Palestinian leader Mahmud Abbas in the West Bank, later met Israeli Prime Minister Ariel Sharon on Sunday.
Dead Sea dying
Environmental experts have repeatedly warned that the Dead Sea - the lowest and most saline place on earth - is in danger of drying up as Jordan, Israel and the Palestinians divert the Jordan River, which feeds it, for agricultural needs.
Sharon and al-Mulki discussed
the canal cooperation project
Between 1960 and 2000, the Dead Sea dropped from 392 metres below sea level to 412 metres, according to Ilias Salama, geology professor at the University of Jordan.
He has warned that by 2010 the Dead Sea could have lost one third of its area compared to its nearly 1000sq km at the beginning of the 1960s.
Jordan, Israel and the Palestinian Authorities had reached an initial agreement to conduct a feasibility study to build the canal, but the project was halted by the onset of the Palestinian uprising against Israeli occupation.