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Livni is expected to tell Mubarak that Israel is prepared to consider offers, but she would also complain about the ongoing rockets and mortars attacks against Israel over the past month.
The foreign minister is also set to discuss with Mubarak the ongoing Israeli-Palestinian peace negotiations.
The invitation was extended to Livni on Sunday by her Egyptian counterpart, Ahmed Aboul Gheit, in a telephone conversation, according to the on-line report of local daily Ha'aretz.
Earlier Monday, Livni told U.S. Secretary of State Condoleezza Rice on phone that Israel would not continue to tolerate rocket attacks from Gaza.
"The situation in which Hamas continues to fire at Israelis and Israeli communities is unacceptable," said Livni.
Meanwhile, Livni also instructed Israel's ambassadors around the world to launch a global effort in a bid to secure backing for the anticipated operation in the Gaza Strip.
A six-month truce, brokered by Egypt between Israel and Gaza militant groups, expired last Friday following failed efforts to resume the truce or extend it for another six months.