Arab outrage over President Donald Trump's decision to move the American embassy in Israel to Jerusalem had prompted the cancellation of several planned meetings ahead of Pence's trip, originally scheduled for December.
Abdullah, a key US ally, said he had "continuously voiced over the past year... my concerns regarding the US decision on Jerusalem that does not come as a result of a comprehensive settlement to the Palestinian Israeli conflict".
Israel occupied the West Bank in 1967 and later annexed east Jerusalem in a move never recognised by the international community.
The US move to recognise the city as Israel's capital broke with decades of international consensus that the city's status should be settled as part of a two-state peace deal between Israel and the Palestinians.
Israel claims all of Jerusalem as its united capital, while the Palestinians see the eastern sector as the capital of their future state.
Pence will head to Israel later today for a two-day visit, during which he can expect a warm welcome from Prime Minister Benjamin Netanyahu and President Reuven Rivlin.
Pence -- a devout Christian -- will visit the Western Wall, one of the holiest Jewish sites in Jerusalem's Old City, and pay his respects at the Yad Vashem Holocaust memorial.
He will also deliver a speech to Israel's parliament on Monday. A coalition of Arab parties said it would boycott the address, calling Pence "dangerous and messianic".
The leaders of both Egypt and Jordan, the only Arab states that have peace treaties with Israel, would be key players if US mediators ever manage to revive a stalled Israeli-Palestinian peace process, as Trump says he wants.
Speaking in Amman today, 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.
"We hope that the US will reach out and find the right way to move forward in these challenging circumstances," he said.
Sisi 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".
The international community considers east Jerusalem illegally occupied by Israel and all embassies are currently in commercial capital Tel Aviv.
Pence's trip has also been overshadowed by the White House's decision to freeze tens of millions of dollars in aid to the United Nations agency for Palestinians, as well as by a federal government shutdown looming over Washington.
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