The visit, initially scheduled for December before being postponed, is the final leg of a trip that has included talks in Egypt and Jordan as well as a stop at a US military facility near the Syrian border.
Controversy back home over a budget dispute that has led to a US government shutdown has trailed Pence, and he sought to blame Democrats for the impasse during a speech to troops at the military facility on Sunday.
Palestinian president Mahmud Abbas is refusing to meet Pence because of the declaration, making his visit a rare one by a high-ranking US official not to include talks with the Palestinians.
He will meet Israeli Prime Minister Benjamin Netanyahu on Monday before addressing the country's parliament later in the day -- a speech that Israeli Arab lawmakers will boycott, calling Pence "dangerous and messianic".
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On Tuesday, the devout Christian will visit Jerusalem's Western Wall, one of the holiest sites in Judaism. Trump became the first sitting US president to visit the site when he travelled to Jerusalem in May 2017.
The city's status is perhaps the most sensitive in the Israeli-Palestinian conflict, and the Palestinians' reaction to Trump's recognition was an illustration of the importance placed upon it.
Beyond refusing to meet Pence, Abbas has said the United States can no longer serve as mediator in Middle East peace talks and the Palestinians were planning a general strike on Tuesday to protest Trump's declaration.
Unrest since the announcement has left at least 17 Palestinians dead, most of them killed in clashes with Israeli forces. One Israeli has been killed in that time.
Netanyahu appeared more interested in talking with Pence on other issues, though he stressed "there is no substitute for US leadership".
"We will discuss the efforts of the Trump administration to block Iran's aggression and the Iranian nuclear programme, and of course, advancing security and peace in the region," Netanyahu said ahead of a cabinet meeting on Sunday.
"Whoever truly aspires to realise these goals knows that there is no substitute for US leadership."
Earlier Sunday, Jordan's King Abdullah II, a key US ally, voiced concern over Trump's Jerusalem recognition as Pence visited Amman.
Speaking in Amman, Pence called Trump's Jerusalem move a "historic decision" but said the United States respected Jordan's role as custodian of the city's holy sites.
"The United States of America remains committed, if the parties agree, to a two-state solution. We are committed to restarting the peace process, and Jordan does now and has always played a central role in facilitating peace in the region," Pence said.
Israel claims all of Jerusalem as its capital, while the Palestinians see the eastern sector as the capital of their future state.