The US has rejected global calls for a ceasefire between Israel and the Palestinian group Hamas, arguing it is not the “right answer right now”.
Currently, supplies of food, water, fuel and medicines for Gaza’s 2.2 million residents are dangerously low.
But Israel has vowed there will be no ceasefire until Hamas is dismantled.
“Calls for a ceasefire are calls for Israel to surrender to Hamas, to surrender to terrorism… this will not happen,” Israel’s Prime Minister Benjamin Netanyahu said.
Speaking at a press briefing, Mr Kirby said he was confident more aid trucks would be able to enter Gaza via Egypt.
He said the US had spoken to the Israeli government about increasing the number of lorries crossing the border each day to around 100.
About 45 trucks had entered Gaza through Egypt’s Rafah Crossing on Sunday, Mr Kirby said. But, he conceded more would be needed.
“We know that even that, which is a dramatic improvement over where we are right now, is still not going to be enough,” he told the press briefing.
Philippe Lazzarini, the commissioner-general of UN relief agency UNRWA, previously told the BBC that about 500 trucks a day had entered Gaza before the war started.
Israel has been bombing Gaza since the 7 October Hamas attacks that killed 1,400 people in Israel and saw 229 people taken hostage by Hamas.
More than 8,300 people in Gaza have been killed since Israel’s retaliatory bombing began, according to the Hamas-run health ministry.
Yinam Cohen, Israel’s consul general to the Midwest, said on Monday that one woman held hostage by Hamas; Natalie Raanan, had returned home to Chicago.
Last week, the UN General Assembly overwhelmingly called for an immediate humanitarian truce between Israel and Hamas, which was angrily dismisses by Israel.
On Monday, Mr Lazzarini said the system to provide aid would “fail unless there is political will to make the flow of supplies meaningful, matching the unprecedented humanitarian needs”.
Israel began what Mr Netanyahu called the “second stage” of a war intended to destroy Hamas on Monday, with ground forces expanding their operations inside Gaza after three weeks of intense bombardment.