Although Palestinian president Mahmoud Abbas has not committed himself to resuming talks, Mr Mitchell said the two had had "serious and positive" discussions when they met this week.
Meanwhile Shimon Peres said he hoped the “proximity” talks involving the United States would develop into direct talks.
Speaking during an official visit to Bulgaria, he noted “positive advancements” and said: "I hope it will happen as early as possible and as soon as I hope.”
Mr Peres added that Israel had disengaged from the Gaza Strip in August 2005 "willingly" and was "unwilling to go back".
The Israeli president was given the "Stara Planina", Bulgaria's highest award, while in Sofia. He used the opportunity to praise Bulgarians for their efforts to save Jewish people during the Holocaust.
