Rep. King is expected to meet with Israeli officials, and tour the tunnels as well as places hit by violence.
The prime minister took time out of his schedule to meet with Cuomo just hours before a temporary cease-fire between Israel and Hamas was set to expire.
Cuomo, Assembly Speaker Sheldon Silver and Senate co-leaders Dean Skelos and Jeff Klein will travel to Israel on Tuesday for a two-day visit.
Later Saturday, a silent protest and candlelight vigil organized as a social media movement aimed at uniting Jews and Arabs was expected to be held in Dag Hammarskjold Plaza near U.N. headquarters.
After leaving the violence and fear at home, nearly 100 Israeli and Palestinian teenagers came together at Seeds of Peace.
Despite an ongoing and bloody conflict, hundreds of families left the United States to immigrate to Israel on Monday afternoon.
An Israeli official said Israel hoped to find a diplomatic solution to the crisis as well and signaled Egypt was likely to play a key role in enforcing any truce.
The Sabbath was far from a day of rest in Israel this Saturday, as the military was poised for a ground offensive in Gaza, and protests by supporters of Israel and Palestine pressed on in New York.