Mediators Egypt and Qatar accused Israel of violating humanitarian law by using starvation as a weapon.
The ceasefire's first phase saw a surge in humanitarian aid after months of growing hunger.
Hamas accused Israel of trying to derail the next phase on Sunday, hours after its first phase had ended and called Israel's decision to cut off aid "a war crime and a blatant attack" on a truce that took a year of negotiations before taking hold in January.
In the second phase, Hamas could release dozens of remaining hostages in return for an Israeli pullout from Gaza and a lasting ceasefire. Negotiations on the second phase were meant to start a month ago but haven't begun.
Israel said on Sunday that a new US proposal calls for extending the ceasefire's first phase through Ramadan — the Muslim holy month that began over the weekend — and the Jewish Passover holiday, which ends on April 20.
Under that proposal, Hamas would release half the hostages on the first day and the rest when an agreement is reached on a permanent ceasefire, Israeli Prime Minister Benjamin Netanyahu said.
The militants currently hold 59 hostages, 35 of them believed to be dead.
Netanyahu said Israel was fully co-ordinated with the Trump administration and the ceasefire will only continue as long as Hamas keeps releasing hostages.
Saying the ceasefire has saved countless lives, the International Committee of the Red Cross said that "any unravelling of the forward momentum created over the last six weeks risks plunging people back into despair".
UN humanitarian chief Tom Fletcher called Israel's decision "alarming," noting that international humanitarian law makes clear that aid access must be allowed.
UN Secretary-General António Guterres urged all parties to make every effort to prevent a return to hostilities in Gaza, and called for humanitarian aid to flow back into Gaza immediately and for the release of all hostages, said spokesman Stéphane Dujarric.
Five non-governmental groups asked Israel's Supreme Court for an interim order barring the state from preventing aid from entering Gaza, claiming the move violates Israel's obligations under international law.
"These obligations cannot be condition on political considerations."
The war has left most of Gaza's population of over two million dependent on international aid.
About 600 aid trucks had entered daily since the ceasefire began on January 19, easing fears of famine raised by international experts.
But residents said prices shot up as word of the closure spread.
From the heavily destroyed Jabaliya urban refugee camp, Fayza Nassar said the closure would worsen dire conditions.
"There will be famine and chaos," she said.
Hamas warned that any attempt to delay or cancel the ceasefire agreement would have "humanitarian consequences" for the hostages. The only way to free them is through the existing deal, the group said.
Families of hostages again pressed Israel's government.
"Postponing the negotiation on the deal for everyone's (release) can't happen," Lishay Miran-Lavi, wife of hostage Omri Miran, said in Tel Aviv.
"Hostages don't have time to wait for an ideal deal."
Israel imposed a siege on Gaza in the war's opening days and only eased it under US pressure. UN agencies and aid groups accused Israel of not facilitating enough aid during 15 months of war.
The International Criminal Court said there was reason to believe Israel had used "starvation as a method of warfare" when it issued an arrest warrant for Netanyahu last year. The allegation is also central to South Africa's case at the International Court of Justice accusing Israel of genocide.
Israel has denied the accusations. It says it has allowed in enough aid and blamed shortages on what it called the UN's inability to distribute it. It also accused Hamas of siphoning off aid — an allegation that Netanyahu repeated on Sunday.
Kenneth Roth, former head of Human Rights Watch, said Israel as an occupying power has an "absolute duty" to facilitate humanitarian aid under the Geneva Conventions, and called Israel's decision "a resumption of the war-crime starvation strategy" that led to the ICC warrant.
