A senior Hamas official predicted a ceasefire within days even as Israel and Gaza militants pursued their cross-border attacks into an 11th day on Thursday with Israeli warplanes carrying out new air strikes and Palestinians firing more rockets. U.S. President Joe Biden urged Israeli Prime Minister Benjamin Netanyahu to seek a "de-escalation" on Wednesday on the path to a ceasefire. An Egyptian security source said the sides had agreed in principle to a ceasefire after help from mediators but that details were still being negotiated in secret. "I think that the ongoing efforts regarding the ceasefire will succeed," the Hamas political official, Moussa Abu Marzouk, told Lebanon"s al-Mayadeen TV. "I expect a ceasefire to be reached within a day or two, and the ceasefire will be on the basis of mutual agreement." Qatar-based Al Jazeera television reported that U.N. Middle East peace envoy Tor Wennesland was meeting Hamas chief Ismail Haniyeh in Qatar. But the fighting continued with both Israel and the Islamist militants voicing defiance. Israel carried out over a dozen air strikes on Gaza after midnight, including two that destroyed two houses in the enclave"s south. Medics said four people were wounded in an air strike on the town of Khan Younis in southern Gaza. Israel"s military said its aircraft early on Thursday struck what it said was a "weapons storage unit" located in the Gaza City home of a Hamas official, and "military infrastructure located in the residences" of other Hamas commanders, including in Khan Younis. Rocket sirens blared early on Thursday in the southern Israeli town of Beersheba and in areas bordering Gaza. There were no immediate reports of casualties or damage. Since the fighting began on May 10, Palestinian health officials say 228 people have been killed in aerial bombardments that have worsened Gaza"s already dire humanitarian situation. Israeli authorities put the death toll to date at 12 in Israel, where repeated rocket attacks have caused panic and sent people rushing into shelters. Netanyahu has repeatedly hailed what he has described as support from the United States, Israel"s main ally, for a right to self-defence in battling attacks from Gaza, home to 2 million Palestinians. But Biden put the Israeli leader on notice in a telephone call that it was time to lower the intensity of the conflict. "The president conveyed to the prime minister that he expected a significant de-escalation today on the path to a ceasefire," White House spokeswoman Karine Jean-Pierre told reporters on Wednesday. Washington and several Middle East capitals have sought an end to the violence through diplomacy. The 193-member United Nations General Assembly was due to meet on the conflict on Thursday with the participation of several foreign ministers but was not expected to take action. The U.S. mission said it would not support a French push for a resolution in the 15-member U.N. Security Council, saying it believed such actions would “undermine efforts to de-escalate” violence. Hamas began firing rockets on May 10 in retaliation for what it called Israeli rights abuses against Palestinians in Jerusalem during the Muslim holy month of Ramadan. The rocket attacks followed Israeli police clashes with worshippers at al-Aqsa Mosque in Jerusalem and a court case by Israeli settlers to evict Palestinians from a neighbourhood in Israeli-annexed East Jerusalem. The hostilities are the most serious between Hamas and Israel in years, and, in a departure from previous Gaza conflicts, have helped fuel street violence in Israeli cities between Jews and Arabs. The conflict has also spilled over to the Israel-Lebanon frontier and stoked violence in the occupied West Bank. Four rockets were launched towards Israel from Lebanon on Wednesday, the third such incident since the Gaza conflict began, the military said. There was no claim of responsibility. In the West Bank, Israeli troops shot dead a Palestinian woman who the military said had fired a rifle at troops and civilians. At least 21 Palestinians have been killed in clashes with Israeli troops or other incidents in the WestBank since May 10, Palestinian officials said.