The first phase that took effect on October 10 was meant to bring a surge in humanitarian aid for Gaza, including shelter.
Netanyahu is expected to seek support from Trump to allow Israel to step up military action against the Iran-backed Hezbollah terror group in Lebanon.
He made no public statement as he departed Tel Aviv.
In Gaza, winter rain has flooded camps with ankle-deep puddles as Palestinians displaced by two years of war attempted to stay dry in tents frayed by months of use.
In the southern city of Khan Younis, blankets were soaked and clay ovens meant for cooking were swamped. Children wearing flip-flops waded through puddles. Some people used shovels or tin cans to remove water from tents.
"Puddles formed, and there was a bad smell," said Majdoleen Tarabein, displaced from Rafah in southern Gaza. "The tent flew away. We don't know what to do or where to go."
She and family members tried to wring muddy blankets dry by hand.
"When we woke up in the morning, we found that the water had entered the tent," said Eman Abu Riziq, also displaced in Khan Younis. "These are the mattresses. They are all completely soaked."
At least 12 people, including a two-week-old infant, have died since December 13 from hypothermia or weather-related collapses of war-damaged homes, according to Gaza's Health Ministry, part of the Hamas-run government.
Emergency workers have warned people not to stay in damaged buildings, because they could collapse. But with much of the territory in rubble, there are few places to escape the rain. In July, the United Nations estimated that almost 80 per cent of buildings in Gaza have been destroyed or damaged.
Since the ceasefire between Israel and Hamas began, 414 people have been killed and 1142 wounded in Gaza, according to the Health Ministry.
The overall Palestinian death toll from the war is at least 71,266. The ministry, which does not distinguish between militants and civilians in its count, is staffed by medical professionals and maintains detailed records viewed as generally reliable by the international community.
The Israel-Hamas war began with the Hamas-led attack in southern Israel on October 7, 2023 that killed about 1200 people and saw 251 taken hostage,
Humanitarian deliveries into Gaza are falling far short of the amount called for under the US-brokered ceasefire, according to aid organisations and an Associated Press analysis of the Israeli military's figures.
The Israeli military body in charge of humanitarian aid said in the past week that 4200 trucks with aid entered Gaza, plus eight garbage trucks to assist with sanitation, as well as tents and winter clothing. It refused to elaborate on the number of tents. Aid groups have said the need far outstrips the number that have entered.
Since the ceasefire began, around 72,000 tents and 403,000 tarps have entered, according to Shelter Cluster, an international coalition of aid providers led by the Norwegian Refugee Council.
"People in Gaza are surviving in flimsy, waterlogged tents and among ruins," Philippe Lazzarini, commissioner-general of the top UN group overseeing aid in Gaza, wrote on social media. "There is nothing inevitable about this. Aid supplies are not being allowed in at the scale required."
Though the ceasefire agreement has mostly held, its progress has slowed.
Israel has said it refuses to move to the next phase while the remains of the final hostage are still in Gaza. Hamas has said the destruction in Gaza has hampered efforts to find remains.
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