Pence had been due to travel in December last year, but Arab anger over President Donald Trump's decision to declare Jerusalem Israel's capital saw many planned meetings cancelled.
US won't pay $45 million pledged for Palestinian food aid for now
The deadly protests that erupted at the time have subsided, but Pence may still face a cold welcome in some capitals and concern over the fate of the UN aid agency for Palestinians (UNRWA).
Washington has delayed a $65 million funding package for the cash-strapped body, putting at risk operations to feed, teach and heal thousands of Palestinian refugees.
The Palestinian leadership, already stunned and furious over the Jerusalem decision, has denounced the US administration and had already refused to meet Pence during his planned December trip.
But Pence's press secretary, Alyssa Farah, said the vice president would still meet the leaders of Egypt, Jordan and Israel on the high-stakes four-day tour.
Pence will arrive in Cairo on Saturday for a meeting with Egyptian President Abdel Fattah al-Sisi, heading the following day to Amman for a one-on-one with King Abdullah II.
Both these leaders, whose countries have peace deals and diplomatic ties with Israel, would be key players if US mediators ever manage to get a revived Israeli-Palestinian peace process off the ground, as Trump wants.
They are also key intelligence-sharing and security partners in America's various covert and overt battles against Islamist extremism in the region and Egypt is a major recipient of aid to help it buy advanced US military hardware.
On Monday, he will begin a two-day visit to Israel, where he will meet Prime Minister Benjamin Netanyahu and President Reuven Rivlin and deliver a speech to the Knesset.
He can expect a warm welcome from local politicians after Trump's decision on Jerusalem, which Israelis and Palestinians alike interpreted as Washington taking Israel's side in the dispute over the city.
The State Department has begun to plan the sensitive move of the US embassy to the city, a process that US diplomats say may take years to complete - unless they adopt an interim solution and re-badge an existing American property in the city.
This week reports surfaced that Washington may temporarily designate the US consulate general in Jerusalem as the embassy while the search for a secure and practical site for a long-term mission continues.
This could prove just as controversial as building a new embassy, however, as the building currently serves as the US mission to the Israeli-occupied Palestinian territories in the West Bank and East Jerusalem.
And the facility sits astride the "Green Line" that divides the disputed city.
Aid for millions caught up in US-Palestinian row: UN
A senior State Department official, speaking on condition of anonymity, told reporters that - contrary to reports- Secretary of State Rex Tillerson has yet to make a decision on either a permanent or interim location for the mission.
"That is a process that takes, anywhere in the world, time. Time for appropriate design, time for execution. It is a matter of years and not weeks or months," he said.
"So what you have been seeing, reading, talking about is speculation on decisions still pending, but there was never - and I want to be very clear on this point - there was never any policy intent to slow-roll the issue of an embassy move."
Pence - himself a devout Christian - will visit the Western Wall, one of the holiest sites of Judaism in Jerusalem's Old City, and pay his respects at the Yad Vashem Holocaust memorial.
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