US Senate Republicans and Democrats insisted on Wednesday that any viable cease-fire between Israel and Hamas militants must eliminate the threat posed by Hamas rockets and tunnels.

In a letter to President Barack Obama, three senators — Republican Lindsey Graham and Democrats Chuck Schumer and Ben Cardin — said any cease-fire should create a situation in which Israelis no longer face the threat of brazen terrorist attacks.

The three lawmakers set a high bar for Secretary of State John Kerry, who is in Israel trying to negotiate a cease-fire. Obama administration officials have said Hamas must be denied the ability to fire rockets on Israelis.

“The threats posed by Hamas rockets and tunnels whose only purpose is to kill and kidnap Israelis are intolerable, and Israel must be allowed to take any actions necessary to remove those threats,” the senators wrote. “Any effort to broker a cease-fire agreement that does not eliminate those threats cannot be sustained in the long run and will leave Israel vulnerable to future attacks.”

Days of hostilities have killed hundreds of Palestinians and more than 30 Israelis. Although Kerry reported some progress Wednesday, there was no sign that either side was ready to relent, with heavy fighting and rocket fire continuing.

The three senators strongly defended Israel, saying its military has taken “great pains to avoid unnecessary civilian casualties.” They said the same could not be said about Hamas, whose rockets “have only one purpose: to kill as many innocent Israelis as possible.”

Copyright 2014 The Associated Press