In the Gaza Strip, health officials said Israeli air strikes on Thursday had killed five people in the enclave.
There was no immediate Israeli comment on the violence, the latest to fray the October truce accord.
Trump has parlayed the ceasefire into a broader "Board of Peace" initiative aimed at resolving conflicts globally.
After hosting a signing ceremony for the board in Davos, Switzerland, on Thursday, Trump invited his son-in-law Jared Kushner to present development plans for the Gaza Strip, its densely populated cities and towns now in ruins from two years of war.
"In the beginning, we were toying with (building) a free zone, and then (having) a Hamas zone," Kushner told an audience in Davos of Trump's early plans to rebuild the strip, where nearly the entire two-million population is internally displaced.
"And then we said, you know what? Let's just plan for catastrophic success."
Kushner presented the audience with a slideshow depicting a "master plan" for what he termed a "New Gaza," displayed on a colour-coded map with areas reserved for residential development, data centres and industrial parks.
The slides included an image of a Mediterranean coastline packed with glittering towers akin to those in Dubai or Singapore.
They suggested redevelopment would begin in Rafah in the south, an area under complete Israeli military control.
But they did not address key issues such as property rights or compensation for Palestinians who lost their homes, businesses and livelihoods during the war.
Nor did they address where displaced Palestinians might live during the rebuilding.
Kushner did not say who would fund the redevelopment, which would first require clearing an estimated 68 million tons of rubble and war debris.
A conference will be held in Washington DC in the coming weeks "where we'll announce a lot of the contributions that will be made ... from the private sector," Kushner said, without elaborating.
The slides shown by Kushner were nearly identical to slides leaked to the Wall Street Journal in December.
The newspaper reported then that the US had offered to "anchor" 20 per cent of the redevelopment project, without going into detail.
Trump has floated the idea of transforming the long-impoverished and dilapidated Gaza Strip into the "Riviera of the Middle East".
Kushner's presentation in Davos followed remarks by Ali Shaath, the Palestinian technocrat leader backed by the US government to administer the enclave under Trump's 20-point plan for the Gaza Strip.
A key unfulfilled element of the ceasefire has been the reopening of the strip's key Rafah border crossing with Egypt for the entry and exit of Palestinians.
Shaath, speaking by video link, announced the Rafah crossing would open next week.
"Opening Rafah signals that Gaza is no longer closed to the future and to the war," Shaath said.
Israel, which controls the Gaza side of the crossing, has rejected reopening it until Hamas fulfills its ceasefire obligation of returning the remains of the last hostage held in the territory.
After Shaath's announcement, an Israeli political source said a special effort was being made to return Ran Gvili's remains and that Israel would discuss reopening the crossing starting next week.
