Olmert and Peretz met in Jerusalem to discuss Ashkenazi's candidacy to replace Lt. Gen. Dan Halutz who resigned last week.
The appointment will be brought before the Tirkel committee, which approves senior appointments, and will later be presented to the government.
If the government approves the appointment, Ashkenazi will become Israel's 19th army chief.
Olmert and Peretz said they had confidence in Ashkenazi's ability to fulfill the position successfully, and implement the lessons of the Lebanon war.
The prime minister and the defense minister also lauded the two other candidates for the position, Maj. Gen. Moshe Kaplinsky and Maj. Gen. Benny Ganz, saying both were accomplished and worthy candidates.
The two leaders have asked the deputy army chief to remain in his post.
Ashkenazi. Soon to become lieutenant general (Photo: Shalom Bar Tal)
Olmert’s aides hinted Sunday that the approval of Ashkenazi’s appointment is assured, adding that most of those who consulted the prime minister on the matter suggested he make every effort to keep Deputy Chief of Staff Moshe Kaplinsky, who dropped out of the race, in the army.
A senior IDF official told Ynet Sunday that "although in a sense Gabi Ashkenazi is coming from outside the system, there's a feeling he's part of us, and that he is the right man for the position of army chief."
“He is less obligated, less driven by personal contacts; he is a task-oriented man.
Hanan Greenberg and Attila Somfalvi contributed to the report