"We must be prepared for possible retaliation from the other side." Barak added.
The dead in the attacks included at least two senior commanders of Islamic Jihad's armed wing, prompting the group to threaten to unleash a wave of suicide attacks within Israel.
Earlier in the day, Vice Premier Haim Ramon told Army Radio that "I can tell you that targeted killings in the West Bank have led to a drastic drop in terror attacks ... and in the Gaza Strip it certainly reduces the number of rockets fired into Israel."
Jones is to serve as a mediator between the Israelis and the Palestinians regarding implementation of the first stage of the road map peace plan. He will also be in charge of formulating a strategic plan to stabilize the security situation in the Palestinian Authority.
Political officials said Monday that the purpose of Jones' 24-hour visit to Israel was to familiarize himself with the situation while explaining to the Israeli side exactly what his position entails.
Jones later held talks with Prime Minister Ehud Olmert in Jerusalem and was scheduled to meet Foreign Minister Tzipi Livni later Tuesday and to see Barak again over dinner. He was not expected to make any public statements.
He was named to his post last month by U.S. Secretary of State Condoleezza Rice to advise her on security aspects of the new Israeli-Palestinian peace talks.
That announcement came one day after Israeli and Palestinian leaders, meeting in Annapolis, Maryland, agreed to restart long frozen peace talks. Rice said providing security would be a key to their success.