Hizbullah was expected to mark 40 days since Mugniyah's assassination in a rally in the Lebanese capital of Beirut on Monday afternoon, while Israel declared a heightened state of alert.
"We are in the midst of a much more delicate timing, with more risks, and we will get through them as well," he added.
As for the Palestinian issue and the talk on a truce with Hamas, the defense minister clarified that "Israel will continue to hit the Hamas terror anywhere needed.
"If and when a situation is created in which there is no rocket fire, no terror activity against Israel and no smuggling of rockets into the Strip, the road will be paved for a different reality. Unfortunately, we are still far from that."
Barak in southern Mount Hebron (Photo: Ariel Hermoni)
Barak added that Israel would try and ease restriction on Palestinian businesspeople and on Palestinian President Mahmoud Abbas' security officials at the crossings, as well as advance economic projects in the West Bank.
US Vice President Dick Cheney on Monday also addressed the threats Israel is facing, saying that Hamas, with support from Syria and Iran, is trying to "torpedo" peace between the Palestinians and Israel.
Meeting reporters Monday after having breakfast with Prime Minister Ehud Olmert, Cheney said, "It is clearly a difficult situation, in part, because I think it's true, there's evidence that, Hamas is supported by Iran and Syria and that they're doing everything they can to torpedo the peace process."
AP contributed to this report