GAZA, May 20 (Reuters) - 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.