Blinken also “underscored the importance of avoiding further escalation of the conflict and reaching a diplomatic resolution that allows both Israeli and Lebanese families to return to their homes”, Miller said in a statement.
Gallant also met CIA chief William Burns, the key US point man in negotiations to free hostages from Hamas.
“I would like to emphasise that it is Israel’s primary commitment to return the hostages, with no exception, to their families and homes,” Gallant said before starting his meetings.
“We will continue to make every possible effort to bring them home,” he said.
The minister made no further comment as he left the meeting with Blinken, as a few dozen protesters outside the State Department chanted to call him a “war criminal”.
Hamas, which launched the conflict with its October 7 attack on Israel, has come back with its own demands, and the United States hopes the gaps can be bridged.
Netanyahu, who has faced major protests calling for him to accept the deal, in recent days has annoyed the Biden administration by accusing Washington of cutting back arms and ammunition deliveries.
Gallant took a different tack, saying: “The alliance between Israel and the United States, led by the US over many years, is extremely important.”
Other than Israel’s own military, “our ties with the US are the most important element for our future from a security perspective”, he said.
Biden, who has faced criticism from parts of his own base over his support for Israel, held back a shipment that included heavy 2,000-pound bombs.
Netanyahu – who has close relations with Biden’s rivals in the Republican Party – told a cabinet meeting on Sunday that there was a “dramatic drop in the supply” of US weapons around four months ago.
Asked about his latest remark, Miller told reporters: “I don’t understand what that comment meant at all.”
“We have paused one shipment of high-payload munitions. That shipment remains on pause.
“There are other weapons that we continue to provide Israel, as we have done going back years and years, because we are committed to Israel’s security. There has been no change in that.”
Miller said the United States would also press Israel to work on longer-term arrangements after the end of the fighting.
“We don’t want to see in Rafah what we’ve seen in Gaza City and what we’ve seen in Khan Younis, which is the end of major combat operations and then the beginning of Hamas reasserting control,” he said, referring to two other major cities targeted by Israel earlier in the war.
Meanwhile in Israel on Monday, the US ambassador to Israel and German’s foreign minister called for a reformed Palestinian Authority to play a role in post-war Gaza at a summit in the coastal city of Herzliya.
Speaking on the “day after” the war in Gaza, US ambassador Jacob Lew highlighted the need for “civil order, civil administration”, for the coastal Palestinian territory, and the US government’s belief that “the Palestinian Authority has to be part of that”.
Lew stressed the need to reform the Ramallah-based Palestinian government to meet Israeli security concerns: “We’ve got to figure out how to get those people to work in a way that meets everybody’s needs. I think that’s possible.”
The US diplomat reiterated his government’s support for a two-state solution that would see the creation of a Palestinian State.
“A future that provides for security and dignity for the people of Gaza and the West Bank, that is a safer future”, he said.
“To call that a victory for Hamas, it has it backwards”, he added, addressing Israeli claims that statehood would be a reward for Hamas’s unprecedented October 7 attack that led to the death of 1,195, most of them civilians, according to an Agence France-Presse tally based on official Israeli figures.
German Foreign Minister Annalena Baerbock was also at the conference that took place at Herzliya’s Reichman University campus, along with several Israeli military figures.
Baerbock echoed Lew’s remarks on a two-state solution, stating that “pursuing the vision of two states, living side by side, in peace and prosperity, remains the best path towards lasting security”.
Addressing Israeli security concerns, she said the PA (Palestinian Authority) needs to reform.
But, she said: “It’s dangerous and self-defeating to destroy and destabilise established PA structures”, referring to “the West Bank, where the illegal expansion of settlement projects is doing exactly that”.