The visit comes with both Palestinian president Mahmud Abbas and Israeli Prime Minister Benjamin Netanyahu.
The visit comes with both Palestinian president Mahmud Abbas and Israeli Prime Minister Benjamin Netanyahu not in position to make major concessions, some analysts say, and no details have emerged of how Trump's team would overcome that.
Trump also faces a range of crises in addition to controversies at home that may make it difficult for him to focus on the complexities of a major Israeli-Palestinian peace push.
"President Trump has made it clear that it is a top priority for him to work toward achieving a comprehensive and lasting peace agreement between Israelis and Palestinians," a US official said.
"He remains optimistic that progress toward a deal can be achieved."
The visit is part of a regional tour by Kushner, who is also Trump's son-in-law, Trump aide Jason Greenblatt and Deputy National Security Adviser Dina Powell.
They have also held talks with Egyptian, Saudi, Emirati, Qatari and Jordanian officials.
"I think (Israeli-Palestinian conflict) clearly remains important, important enough that senior officials continue to engage on it, including Jared Kushner," Dan Shapiro, US ambassador to Israel under Barack Obama, told journalists this week.
"But given the very poor prospects of a significant political breakthrough, I'd be surprised it if warrants a major investment by the president."
Palestinian leaders have grown frustrated with the White House after initially holding out hope that Trump could bring a fresh approach to peace efforts despite his pledges of staunch support for Israel.
Trump aides have held a series of meetings with both sides, portraying them as hearing out concerns before deciding on a way forward, while the US president himself visited Israel and the Palestinian territories in May.
But Palestinian leaders note that the White House has not even said clearly whether its focus will be a two-state solution to the conflict, which has been longstanding US policy.
The two-state solution envisions an independent Palestinian state alongside Israel and has been the focus of international diplomacy for years.
When Trump met Netanyahu at the White House in February, he said he would support a single state if it led to peace, delighting right-wing Israelis who want to annex most of the West Bank, but raising deep concern among Palestinians.
Signalling their frustration, some Palestinian leaders have spoken of taking a harder line in recent days.
Ahmed Majdalani, a senior Palestinian Liberation Organisation official who is close to Abbas, told AFP on Thursday that one option if no progress is reached would be to dissolve the Palestinian Authority -- a threat that has been made in the past.
That would in theory leave Israel with the responsibility of governing and providing services to Palestinian cities in the occupied West Bank.
But at the same time, Majdalani said they could also unilaterally declare Palestinian statehood.
He said it was an option under consideration because "the American administration has not presented any initiative until now, while the Israelis continue with their settlement activities and refuse to abide by obligations they signed up to."
Netanyahu is meanwhile under pressure from his right-wing base not to make any concessions to the Palestinians and to continue Israeli settlement building, and there is little incentive at the moment for him to change course, some analysts say.
He is also facing a graft investigation that limits his room for political manoeuvre, Shapiro noted.
Shapiro, currently a fellow at the Institute for National Security Studies think-tank in Tel Aviv, said the focus should instead be on short-term goals such as improving the Palestinian economy in order to keep the possibility of a two-state solution alive.
"I believe (Trump's) leverage has declined considerably, at least from the point-of-view of getting major concessions or a commitment to a major programme toward two states from the leaders, so that's why I think the shift should come to the more practical on-the-ground steps," he said.