Secretary of State John Kerry is heading back to the Middle East as the Obama administration attempts to bolster regional efforts to reach a ceasefire and sharpens its criticism of Hamas in its conflict with Israel.

The State Department said Kerry would leave early today for Egypt, where he will join diplomatic efforts to resume a truce that had been agreed to in November 2012. In a statement Sunday evening, department spokeswoman Jen Psaki called the U.S. and international partners “deeply concerned about the risk of further escalation, and the loss of more innocent life.”

The Obama administration has toned down its earlier rebuke of Israel for attacks on the Gaza Strip that have killed civilians, including children, although both President Barack Obama and Kerry expressed concern about the rising death toll.

The U.S. will urge the militant Palestinian group to accept a cease-fire agreement that would halt nearly two weeks of fighting with Israel.

Cairo has offered a cease-fire plan that is backed by the U.S. and Israel. But Hamas has rejected the Egyptian plan and is relying on governments in Qatar and Turkey for an alternative proposal. Qatar and Turkey have ties to the Muslim Brotherhood, which is also linked to Hamas but banned in Egypt.

Making the rounds of Sunday talk shows, Kerry pointed to Hamas’ role in the violence.

“It’s ugly. War is ugly, and bad things are going to happen,” Kerry told ABC’s “This Week.” But, he added, Hamas needs “to recognize their own responsibility.”

Both Obama and Kerry said Israel has a right to defend itself against frequent rocket attacks by Hamas from the Gaza Strip. Kerry accused Hamas of attempting to sedate and kidnap Israelis through a network of tunnels that militants have used to stage cross-border raids.

He said on CNN’s “State of the Union” that Hamas must “step up and show a level of reasonableness, and they need to accept the offer of a cease-fire.”

Then, Kerry said, “we will certainly discuss all of the issues relevant to the underlying crisis.”

Obama, in a telephone call Sunday, told Israeli Prime Minister Benjamin Netanyahu that Kerry was coming to the Mideast and condemned Hamas’ attacks, according to a White House statement.

U.S. officials made clear, however, that Hamas could bring relief to the Palestinian people if it agrees to a cease-fire proposed by Egypt — a view that Netanyahu is pushing as well.

Republican Sen. Lindsey Graham, a member of the Senate Armed Forces Committee, urged Israel to “stay as long as you need to stay, go wherever you need to go, do deal with a viper’s nest called Hamas.”

“If it’s left up to Hamas, thousands of Israelis would be dead,” Graham, R-S.C., told NBC’s “Meet the Press.”