A spokesman for Egyptian President Mohamed Morsy said the Arab League will meet Saturday in emergency session to discuss the violence.
"Egypt is taking all diplomatic measures with all parties involved to reach some sort of immediate truce or cease fire," Yaser Ali added.
A senior official in U.S. President Obama's administration told CNN that the White House is asking Egypt and Turkey -- two nations that have influence with Hamas -- to urge the group to de-escalate the rocket attacks.
But a Hamas deputy foreign minister told CNN: "I am in touch with the Egyptians they are very angry and very upset because they feel that Israel put a knife in their back" by attacking sites in Gaza.
Egypt's Prime Minister Hesham Kandil will travel on Friday morning to Gaza with a team of presidential advisers and ministers to meet with Palestinian officials.
U.N. Secretary-General Ban Ki Moon also will go to Egypt and Israel next week, because of the rising tensions between Israel and Hamas, a Western diplomat told CNN. The diplomat said the Secretary General has canceled a trip to Mozambique, Botswana, Seychelles and Mauritius to go to the Middle East.