Controversy over President Donald Trump's decision to move the American embassy in Israel to Jerusalem had led to the cancellation of a number of planned meetings ahead of the trip originally scheduled for December.
While the deadly protests that erupted in the Palestinian territories at the time have subsided, concerns are mounting over the future of the UN aid agency for Palestinians (UNRWA).
Washington has frozen tens of millions of dollars of funding for the cash-strapped body, putting at risk operations to feed, teach and heal hundreds of thousands of Palestinian refugees.
But the vice president's press secretary, Alyssa Farah, said he would still meet the leaders of Egypt, Jordan and Israel on the high-stakes four-day tour.
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Pence is scheduled to hold talks with Egyptian President Abdel Fattah al-Sisi today before travelling to Amman for a one-on-one meeting with King Abdullah II tomorrow.
The trip had been pushed back in December as a crunch tax vote loomed on Capitol Hill.
The leaders of both countries, the only Arab states that have peace treaties with Israel, would be key players if US mediators ever manage to get a revived Israeli-Palestinian peace process off the ground, as Trump says he wants.
Sisi, one of Trump's closest allies in the region, had urged the US president before his Jerusalem declaration "not to complicate the situation in the region by taking measures that jeopardise the chances of peace in the Middle East".
Ahmed al-Tayeb, the grand Imam of Al-Azhar, Egypt's highest institution of Sunni Islam, cancelled a meeting with Pence in protest at the Jerusalem decision.
After Jordan -- the custodian of Muslim holy sites in Jerusalem -- Pence will head to Israel for talks with Prime Minister Benjamin Netanyahu on Monday.
He will also deliver a speech to parliament and meet President Reuven Rivlin during the two-day visit.
Pence can expect a warm welcome after Trump's decision on Jerusalem, which Israelis and Palestinians alike interpreted as Washington taking Israel's side in the dispute over the city.
Israel occupied the West Bank in 1967 and later annexed east Jerusalem in a move never recognised by the international community.
The international community considers east Jerusalem illegally occupied by Israel and currently all countries have their embassies in the commercial capital Tel Aviv.
The State Department has begun to plan the sensitive move of the US embassy to Jerusalem, a process that US diplomats say may take years to complete.
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.
And the facility sits astride the "Green Line" that divides Jerusalem.
A senior State Department official, speaking on condition of anonymity, told reporters that 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.