By Alexander Cornwell and Nidal al-Mughrabi KIRYAT GAT, Israel (Reuters) -The U.S. increased pressure on Hamas on Tuesday to disarm in the next phase of an already fragile Gaza ceasefire as President Donald Trump pushed to cement an end to the devastating conflict.

An Israeli security official said the transfer of aid into the territory is halted "until further notice," the first major test of the ceasefire.

The group still commands thousands of fighters, but the war has taken a toll on its weapons supplies, and its political future is uncertain.

Israel has accused Hamas of attacking Israeli forces in southern Gaza with the military carrying out airstrikes in the city of Rafah, the first major test of the US-brokered ceasefire.

Trump said on Monday that the US would destroy Hamas if the militant group didn’t continue to honor the ceasefire with Israel.

President Donald Trump is suggesting he could call on Israel to release imprisoned Fatah leader Marwan Barghouti, the most popular and potentially unifying Palestinian leader, as the United States aims to fill a leadership vacuum in postwar Gaza.

The Trump peace plan calls for an international security force in the Gaza Strip, but countries that might send troops are wary of danger, an unclear mission and being seen as occupiers.

The U.S. State Department says it has “credible reports” that Hamas could violate the ceasefire with an attack on Palestinian civilians in Gaza.

Hamas politburo member Mohammed Nazzal also said the group was ready for a ceasefire of up to five years to rebuild devastated Gaza.

Palestinian-American mediator Bishara Bahbah detailed new messages from Hamas to the White House and outlined challenges in implementing the Trump-backed Gaza ceasefire plan. Al-Ain news in the UAE recently published an article that included an interview with a key individual who may have insight into what comes next in Gaza.