Biden calls for 'significant de-escalation today' in 4th call with Israel's Netanyahu

President Joe Biden spoke to Prime Minister Benjamin Netanyahu for the fourth time in a week, calling Israel's long-serving leader on Wednesday to say he "expected a significant de-escalation today on the path to a ceasefire," according to the White House.

After their conversation, Netanyahu again resisted global calls for an immediate halt to the hostilities between Israeli security forces and Hamas, the militant group that governs the Palestinian people of Gaza. In a week and a half of fighting, hundreds have been killed and thousands wounded.

Biden has faced growing pressure from other world leaders, human rights groups and the progressive faction of his own party to push Netanyahu to stop Israeli strikes on Gaza. After speaking Monday, Biden for the first time backed a cease-fire, according to a White House account of the call.

But their latest call was new for the deadline Biden appeared to lay out in use of the word "today" in calling for "a significant de-escalation." The White House readout was the most strongly worded yet from the U.S. side, even as Biden has repeatedly backed Israel's right to self defense against Hamas's constant barrage of rocket fire.

"The two leaders had a detailed discussion on the state of events in Gaza, Israel's progress in degrading the capabilities of Hamas and other terrorist elements, and ongoing diplomatic efforts by regional governments and the United States," the White House said.

Hours later, Netanyahu seemed to rebuff Biden, saying, "I am determined to continue this operation until its objective is achieved: To restore quiet and security to you, citizens of Israel." He added that he "especially appreciate(s) the support of our friend U.S. President Joe Biden for the state of Israel's right to self-defense."

Biden has faced criticism at home from the left and right, with Republicans accusing him of not defending Israel enough.

His administration has consistently defended what it calls "quiet, intensive diplomacy" to halt the hostilities, pointing to rounds of calls between Secretary of State Antony Blinken, National Security Adviser Jake Sullivan, and other senior U.S. officials and their regional counterparts. The administration also deployed its Deputy Assistant Secretary of State for Israeli-Palestinian issues Hady Amr to the region.

The White House declined to provide more details of the Wednesday call. Aboard Air Force One, principal deputy press secretary Karine Jean-Pierre rebuffed several questions from reporters, including why Biden appeared to be intensifying his tone now and what the U.S. would do if Netanyahu didn't meet this new apparent deadline.

During their call Monday, Biden took a tougher tone with Netanyahu and had a firmer message than he has publicly and on previous private calls, sources told ABC News Tuesday. He conveyed the message that he could only provide Netanyahu's government cover for so long from the growing calls in Congress and around the world for Israel to take a different approach to Gaza.

While progressive lawmakers have been condemning Israel's action since fighting erupted last week, a majority of Democratic senators called for an immediate cease-fire earlier this week, building pressure on Biden to do the same.

He has continued to resist that call, even as the death toll mounts with each day. At least 219 people, including 63 children, have been killed by Israeli airstrikes in the last 10 days, while 1,530 others have been wounded, according to the Palestinian Ministry of Health. Across the border, at least 12 people, including one child, have been killed by Hamas's rocket fire, with another 324 injured, according to the Israeli Defense Forces.

While Israel has resisted a cease-fire, Hamas's leadership has now said it's open to one.

"We informed all parties that we would accept a mutual ceasefire between Israel and Hamas with two conditions," Dr. Basem Naim, a former Palestinian health minister who is now head of Hamas's international relations council, told ABC News on Tuesday evening.

Naim said those conditions are that Israeli forces "stop incursions into the Al-Aqsa compound," Islam's third holiest site in Jerusalem's Old City where Muslims worship, and that Israel "stop the forced evacuation of the Palestinian residents" of Sheikh Jarrah, a historically Palestinian neighborhood in East Jerusalem where Israeli settlers have filed court cases to seize their homes.

Israeli forces' assault on Al-Aqsa nearly two weeks ago and the ongoing litigation over Sheikh Jarrah evictions precipitated this latest round of violent fighting -- the latest deadly spasm of the decades-old conflict.

ABC News's Cecilia Vega and Ben Gittleson contributed to this report from the White House and Nasser Atta from Jerusalem.