"There are ongoing attempts to promote a new hostage deal and there are promising early signs of possible progress," Gantz said in a televised press briefing.
"We will not stop looking for a way and we will not miss any opportunity to bring our girls and boys home."
But he added that if no new deal were struck, the Israeli military would keep fighting in Gaza even into the Muslim holy month of Ramadan, which begins next month.
Benny Gantz says "there are promising early signs of possible progress" on a hostage deal. (AP PHOTO)
"If a new hostage deal is not achieved, we will continue operating also during Ramadan," he said.
Meanwhile, the United Kingdom and Jordan air-dropped four tonnes of aid including medicines, fuel and food to Tal al-Hawa Hospital in northern Gaza, the UK's Foreign Office said on Wednesday.
The UK-funded aid was delivered by the Jordanian air force.
"Thousands of patients will benefit and the fuel will enable this vital hospital to continue its life-saving work," UK Foreign Secretary David Cameron said in a statement.
"However, the situation in Gaza is desperate and significantly more aid is needed, and fast. We are calling for an immediate humanitarian pause to allow additional aid into Gaza as quickly as possible and bring hostages home."
Israeli MPs voted on Wednesday to back Prime Minister Benjamin Netanyahu's rejection of any "unilateral" recognition of a Palestinian state as international calls have grown for the revival of Palestinian statehood negotiations.
Issued amid the war in Gaza between Israel and Hamas, the symbolic declaration also received backing from members of the opposition, with 99 of 120 MPs voting in support, the Knesset representative said.
The Israeli position says that any permanent accord with the Palestinians must be reached through direct negotiations between the sides and not by international dictates.
"The Knesset came together in an overwhelming majority against the attempt to impose on us the establishment of a Palestinian state, which would not only fail to bring peace but would endanger the state of Israel," Netanyahu said.
The vote drew condemnation from the Palestinian foreign ministry, which accused Israel of holding the rights of the Palestinian people hostage by forceful occupation of territories where Palestinians seek to establish a state.
"The ministry reaffirms that the State of Palestine's full membership in the United Nations and its recognition by other nations does not require permission from Netanyahu," it said in a statement.
Little progress has been made towards achieving a two-state solution - a Palestinian state in the occupied West Bank and in Gaza alongside Israel - since the signing of the interim Oslo Accords in the early 1990s.
Among the obstacles impeding Palestinian statehood are expanding Israeli settlements in territories Israel captured in the 1967 Middle East war.
Most countries regard the settlements, which in many areas cut Palestinian communities off from each other, as a violation of international law.
Since the outbreak in October of the Gaza war, the United States has been trying to promote steps toward the creation of a Palestinian state as part of a broader Middle East deal that would include Saudi Arabia and other Arab states officially normalising relations with Israel.
