Top military officers praised IDF Chief of General Staff Lt.-Gen. Dan Halutz's decision to resign, saying Wednesday that it was the first step towards the complete rehabilitation of the IDF following the failures and disappointing outcome of the summer's war in Lebanon. Prime Minister Ehud Olmert and Defense Minister Amir Peretz said Wednesday that they hoped to reach an agreement on a suitable candidate to replace Halutz. Senior defense officials told The Jerusalem Post that Peretz and Deputy Defense Minister Ephraim Sneh were leaning towards recommending Defense Minister Dir.-Gen. Maj.-Gen. (res.) Gabi Ashkenazi for the job. Other candidates include Deputy Chief of General Staff Maj.-Gen. Moshe Kaplinsky, recommended by Halutz and reportedly favored by Olmert, as well as OC Ground Forces Command Maj.-Gen. Benny Gantz and Maj.-Gen. (res.) Ilan Biran. "This is a new beginning that needs to be used to get the IDF back in order and ready for future challenges," a high-ranking officer told the Post. "Halutz's decision was brave, but also necessary so the military could move on from the war in the summer." Olmert said that the process of selecting a new chief of staff would be completed as soon as possible, with the Prime Minister's Office expecting that a new chief of staff would be named either by the end of next week, or the beginning of the week after. Peretz's office said that the defense minister preferred to submit the name of a candidate for the cabinet's approval this coming Sunday. In his first appearance since announcing his resignation after midnight Tuesday, Halutz spoke Wednesday evening at a Navy ceremony in Haifa and explained his decision, which, he said, was based on "deep-rooted values, those of strong ethics, loyalty to the organization and integrity." "I served the army responsibly for over four decades, and this responsibility continued in the last few months," Halutz told the crowd to the sounds of applause and cheering. "It is this responsibility that led me to announce my resignation." Peretz, also present at the ceremony, praised Halutz as a soldier and a commander and stressed that the new chief of staff would be chosen without delay. "The chief of general staff [Halutz] has conducted the process necessary to transform the crisis of the Lebanon war into leverage for change," Peretz said in reference to the 50-some internal military probes Halutz appointed to investigate the military's performance during the war. Peretz also sent out a warning to Israel's enemies: "Do not misinterpret the chief of staff's resignation. Do not make the mistake of seeing this as a sign of weakness - it is a sign of our national strength." A former chief of staff told the Post that Halutz's decision was "brave," but should have been made six months ago, immediately following the war. The former general said he thought that Halutz decided to resign now after receiving word that the Winograd Commission planned to blame him for the war's failures. He also predicted that Halutz had decided to step down before testifying to the commission in order to more easily accuse Olmert and Peretz for the war's outcome. Olmert spoke with Peretz twice on Wednesday about the manner in which the next chief of staff will be selected. Olmert, who said Wednesday he would meet with a host of officials ranging from former prime ministers to former chiefs of staff, will begin the process Thursday by meeting with former prime ministers Shimon Peres, Binyamin Netanyahu and Ehud Barak, and with former defense ministers Binyamin Ben-Eliezer and Shaul Mofaz. Olmert issued a statement Wednesday lauding Halutz, and saying he did not accept his request that he reconsider his resignation. "Lt.-Gen. Dan Halutz is one of Israel's greatest soldiers," the statement read. "He served in the IDF for 40 years. He was an outstanding IAF pilot. He participated in dozens of combat actions in which he led those under his command to unprecedented achievements." Olmert praised Halutz as a "brave and exemplary person who faithfully served his country with unparalleled personal sacrifice." Olmert said Halutz wanted to "lead the IDF through an unprecedented series of investigations in order to draw the necessary lessons from the fighting in Lebanon and in order to allow the IDF to best prepare for future challenges. Now, as the investigations stage comes to an end, he has decided to finish his duties and allow his replacement to implement the necessary changes," Olmert said. Foreign Minister Tzipi Livni, who is currently on a visit to Japan, said she has a "great deal of admiration" for Halutz and the step he took. She said that Halutz's decision to step down "reflects his values as a person and as an IDF officer." Gil Hoffman contributed to the report.