US President Barack Obama told Prime Minister Binyamin Netanyahu in a phone conversation that Israel must immediately stop all military activities in Gaza, and said Jerusalem was not in a position to pick the mediators of a cease-fire, Channel 1 reported Tuesday night.According to what Channel 1 said was a partial transcript of the Sunday phone call, when Netanyahu asked what Israel would get from stopping its military operation, Obama said that he believed Hamas would stop the firing of rockets, and that “quiet would be met with quiet.”The White House quickly issued a denial, with Ben Rhodes, the deputy national security adviser, calling the supposed transcript of the call “totally false.”“Neither the reports nor alleged transcript bear any resemblance to reality,” the National Security Council press office immediately posted on its Twitter account. It was “shocking and disappointing someone would sink to misrepresenting” a private conversation between Obama and Netanyahu, the press office said.Netanyahu, according to the report, replied to Obama that Hamas was a terrorist organization committed to Israel’s destruction, and one that had already violated five cease-fires.Obama reportedly repeated his call for an immediate end to the IDF operation, saying the pictures of the destruction from the Gaza Strip were distancing the world from Israel. He said that a week after the operation ended, Turkey and Qatar would negotiate with Hamas on the basis of the understanding that ended Operation Pillar of Defense in 2012.When Netanyahu said that Turkey and Qatar were Hamas’s biggest supporters, and it was impossible for Israel to rely on them, Obama reportedly said that he would rely on them, and that Israel was not in a position to chose the mediators. The ball was in Israel’s court, Obama told Netanyahu, according to the report, and it must stop the military operation.Meanwhile, Hamas’s rocket fire on Israel and Israel’s bombardment of Gaza continued unabated Tuesday night, even amid reports that Israel, Hamas, the Palestinian Authority and Egypt have agreed to a cease-fire framework.Channel 2 reported that under the terms of the deal, there would be a cease-fire for between 24 and 72 hours, during which Israel would continue to decommission Gaza’s attack tunnels. After that, if the cease-fire holds, the sides would meet and hold indirect talks in Cairo to hammer out a long-term accord.This framework is similar to the Egyptian proposal put forward a few days after Operation Protective Edge began 22 days ago, and which Hamas rejected.An Israeli government official denied, however, that any agreement had been reached.“The fighting continues,” he said. “The military campaign is ongoing, but the diplomacy is also ongoing.”The official said Israel has always accepted the Egyptian proposal, but would not say whether Jerusalem would accept anything different.Hamas, through Qatar and Turkey, is demanding in exchange for a cease-fire that a number of conditions be met, including opening Gaza’s border crossings, lifting Israel’s blockade, allowing the transfer of funds to pay Hamas salaries, and the release of Hamas prisoners released in the exchange for IDF tank gunner Gilad Schalit but rearrested last month following the kidnapping and murder of three Israeli teenagers. Additional contradictions between Netanyahu and US Secretary of State John Kerry continued to surface on Tuesday, with Kerry saying the prime minister asked him on Monday night to work toward a humanitarian cease-fire, and a diplomatic source in Jerusalem saying it was Kerry who raised the issue.Washington has expressed dismay in recent days over the harsh criticism in Israel of a draft cease-fire proposal the US presented on Friday. Israel felt the proposal fell far short of meeting its security requirements and leaned toward Hamas’s demands, giving the organization a standing it had not hitherto enjoyed. One of Israel’s main concerns with the draft was that it did not spell out that Israel would be able to continue to work against the tunnels during the proposed weeklong ceasefire.Kerry said that the plan put forth did, in fact, allow Israel “to continue to deal with its tunnels.”He also said that what the US was proposing did not deviate at all from the Cairo proposal.“No variation, no deviation. We’ve been in touch with the Egyptians; we have honored the Egyptian concept. If there is a negotiation, it would be in Cairo,” he said. “It would be entirely without preconditions, and it would not prejudice Israel’s ability to defend itself.”Repeating what he said a number of months ago when Defense Minister Moshe Ya’alon slammed his efforts at brokering an Israeli-Palestinian peace accord, Kerry said of the Israeli criticism that “I’ve taken hits before in politics. I’m not worried about that.”Now, like then, he highlighted his 29 years of a perfect pro-Israel voting record in the US Senate, adding that “I will not take a second seat to anybody in my friendship or my devotion to the protection of the State of Israel.”Kerry, who said that in recent days he has talked to Netanyahu two to four times a day, added that on Monday night, the prime minister raised the issue of a cease-fire, “as he has consistently.He has consistently said that he would embrace a cease-fire that permits Israel to protect itself against the tunnels and obviously not be disadvantaged for the great sacrifice that they have made in order to be able to protect themselves thus far.”The secretary of state said that if it were not for Netanyahu’s commitment to a cease-fire, the US would not be expending the effort to bring one about.“Now, either I take his commitment at face value, or someone is playing a different game here, and I hope that’s not the fact,” he said.A senior official in the Prime Minister’s Office, however, contradicted this telling of events, saying it was Kerry who raised the issue of a cease-fire to Netanyahu.According to this official, the prime minister told Kerry the IDF operation in Gaza, including the actions against the tunnels, was necessary for the security of Israel and would continue. He added that there was a need to continue acting against the tunnels “until the job was completed.”In a related development, Chile and Peru followed Brazil’s lead from last week and recalled their ambassadors for consultation in protest over Israel’s operation in Gaza. Once Brazil recalled its ambassador, it was widely expected that a number of other South American countries would do the same.