Bringing the hostages home is "the right thing to do", Gallant told foreign journalists.
"Achieving an agreement is also a strategic opportunity that gives us a high chance to change the security situation on all fronts," he said.
Israel, which has been at war with Palestinian militants in Gaza since Hamas's October 7 attack, is also engaged in near-daily clashes with Lebanon's Hezbollah movement on its northern border with Lebanon.
Urging the international community to keep up the pressure on Hamas to reach an agreement, Gallant said he firmly supported the first stage of a three-phase ceasefire deal announced by US President Joe Biden on May 31, hoping to build on it for an eventual end to the war.
"Israel should achieve an agreement that will bring about a pause for six weeks and bring back hostages," Gallant told journalists at a sit-down on Monday at his office. His remarks were released for publication on Tuesday.
Gallant also said Hamas's military capabilities had been severely damaged after more than 11 months of war and that it no longer existed as a military formation in Gaza.
"Hamas as a military formation no longer exists. Hamas is engaged in guerrilla warfare and we are still fighting Hamas terrorists and pursuing Hamas leadership," he said.
His comments came as mediators the United States, Qatar and Egypt struggle to reach an agreement between Israel and Hamas to end the war in Gaza, which has killed nearly 41,000 people.
- At odds with Netanyahu -
Gallant is among the Israeli officials who have clashed with Prime Minister Benjamin Netanyahu on war policy.
Israeli media last month quoted him as privately telling a parliamentary committee that a hostage release deal "is stalling... in part because of Israel".
Netanyahu's office accused Gallant of adopting an "anti-Israel narrative".
Gallant said Israel's military pressure in Gaza had created the "necessary conditions" for a ceasefire deal.
Biden unveiled a three-phase plan that would see an initial six-week halt in fighting and the release of hostages by Hamas in exchange for an unspecified number of Palestinian prisoners held in Israeli jails.
One of the biggest stumbling blocks has been Netanyahu's insistence on maintaining troops along Gaza's border with Egypt, in a strip of land known as the Philadelphi Corridor.
Netanyahu said last week that retaining control of the corridor was important to stop any arms smuggling into Gaza from Egypt.
Hamas is demanding a complete Israeli withdrawal from Gaza.
- 'Moral obligation' -
Gallant's latest comments come as domestic pressure mounts on Netanyahu to end the war.
Tens of thousands of Israelis have taken to the streets to demand a truce and hostage release deal, with their anger and grief spiking after the recent killing of six hostages whose bodies were found in a Gaza tunnel.
"Israel currently faces a strategic junction. It is an opportunity to fulfil our moral obligation to our citizens by bringing hostages home," Gallant said.
The war, now in its 12th month, broke out after the October 7 attack on Israel, which resulted in the deaths of 1,205 people, mostly civilians, according to official Israeli figures.
Militants also seized 251 hostages at the time, 97 of whom are still held in Gaza, including 33 the Israeli military says are dead.
Israel's retaliatory air, land and sea campaign has so far killed at least 40,988 people in Gaza, according to the Hamas-run territory's health ministry.
The United Nations rights office says most of the dead are women and children.
Since the Gaza war began, Israel has also been engaged in clashes with Iran-backed Lebanese Shiite armed group Hezbollah, a close ally of Hamas.
"We are committed to changing the security situation on the northern front and to bringing our citizens home safely," Gallant said.
The widespread destruction has produced a dire humanitarian situation in Gaza, underscored by the recent confirmation of its first polio case in 25 years.
Gallant touted the military's efforts to facilitate humanitarian assistance.
"Together with international partners, we have planned and executed five humanitarian operations to evacuate ill and wounded children and civilians from Gaza for treatment in third countries. Three additional missions are already underway," he said.
"Since the beginning of the war till September 1st, we have delivered 50,440 trucks of aid."
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