(CNN) -- U.S. Secretary of State Condoleezza Rice and Israeli Foreign Minister Tzipi Livni Friday signed a memorandum of understanding that spells out steps to stop the flow of weapons to Hamas militants in Gaza.
Tzipi Livni met with United Nations Secretary General Ban Ki-Moon Thursday.
The meeting in Washington is one of several diplomatic moves afoot to end the fighting between Israel and Hamas in Gaza.
This comes as the Israeli offensive against Hamas militants continued Friday, with Israeli airstrikes pounding the northern and southern sections of Gaza.
Israel wants to couple any cease-fire agreement with U.S. and international support, including intelligence cooperation to prevent arms smuggling, State Department spokesman Sean McCormack has said. 
Watch more on the latest fighting in Gaza »
Israel on Thursday dispatched senior Defense Ministry official Amos Gilad to Cairo to discuss a cease-fire proposal. A Hamas delegation is also in the Egyptian capital, talking with leaders there who are trying to hammer out a temporary truce.
Egypt has hosted peace talks with leaders from Israel and the Palestinian Authority, and has acted as an intermediary between Hamas and Israel.
Arab and regional diplomats and leaders also have been meeting to deal with the crisis.
Gulf countries met in the Saudi capital of Riyadh on Thursday. Qatar hosted an emergency summit in Doha that included Arab and regional countries, including Iran.
In Kuwait, Arab League foreign ministers were meeting on Friday and Arab leaders then plan to begin meeting on Saturday for an economic summit that is to address in part the reconstruction of the devastated Gaza territory.
Also, U.N. Secretary-General Ban Ki-moon continued his trip through the region as part of the diplomatic effort to secure a truce. He has called for an immediate cease-fire between Hamas and Israel, and said he is encouraged that the Egyptian government is trying to broker a truce.
He met with Israeli officials on Thursday, and condemned an Israeli strike that damaged the U.N. Relief and Works Agency's compound in Gaza City that sparked a massive fire and injured three people.
Once the fighting stops, the two sides can "discuss how to make this cease-fire durable and sustainable," he said.
-- CNN's Caroline Faraj contributed to this report.
