Hamas said it expects a truce within days. German Foreign Minister Heiko Maas is also set to fly to Israel and Palestinian territories for talks over halting hostilities.
A senior Hamas official said that talks with mediators over a cease-fire were underway, predicting that a truce could be reached within days.
Hamas' remarks came as Israel and Gaza militants continued to pursue their cross-border attacks.
"I expect a ceasefire to be reached within a day or two, and the ceasefire will be on the basis of mutual agreement," Moussa Abu Marzouk, told Lebanon's al-Mayadeen TV about reaching a cease-fire.
An Egyptian security source cited by Reuters news agency said the sides had agreed in principle to a cease-fire after help from mediators. However, that details were still under negotiation.
US opposes France's push for UN cease-fire
The United States said it opposed a proposed United Nations Security Council resolution calling for a cease-fire, insisting that it could interfere with other mediation efforts by Washington.
France had drafted the resolution after the US blocked several attempts to have the council issue a public statement calling de-escalation.
"We've been clear and consistent that we are focused on intensive diplomatic efforts underway to bring an end to the violence and that we will not support actions that we believe undermine efforts to de-escalate," a spokesperson for the US Mission to the UN said.
A press statement requires consensus by all 15 council members, but a resolution, which is legally binding, requires at least nine "yes'' votes and no veto by any of the five permanent members.
US President Joe Biden on Wednesday told Israeli Prime Minister Benjamin Netanyahu that he "expected significant de-escalation today on the path to a ceasefire."
But Netanyahu later reiterated that Israeli forces would push ahead with operations to "return calm and security" to Israel.
Germany to hold talks with Israel, Palestinians
Foreign Minister Heiko Maas will travel to Israel and Palestinian territories on Thursday for talks with senior Israeli and Palestinian officials on ending hostilities.
He re-emphasized on Wednesday that Germany supports Israel's right to self-defense as he condemned "rocket terror" attacks on Israeli cities by Hamas.
The top diplomat called for an immediate end of hostilities, and direct talks between Israeli and Palestinian officials for a long-term solution.
"We of the firm conviction that this can only be a negotiated two-state solution," Maas said.
What is the latest on the ground?
Israel's military said its aircraft early on Thursday struck a "weapons storage unit" located in the Gaza City home of a Hamas official, and "military infrastructure located in the residences" of other Hamas chiefs.
In southern Israel and areas bordering Gaza, rocket sirens blared early on Thursday.
Since May 10, Hamas has fired around 4,000 rockets targeting Israel, Israeli officials said.
Gaza health officials said 227 Palestinians have been killed, including 64 children, since the conflict flared.
In Israel, 12 people have been killed, including a 5-year-old boy, a 16-year-old girl and a soldier.