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."
"Jerusalem is key to Muslims and Christians as it is to Jews," he added. "It is key to peace in the region. And key to enabling Muslims to effectively fight some of the root causes of radicalisation."
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 Israeli-Palestinian peace deal.
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 get a revived Israeli-Palestinian peace process off the ground, as Trump says he wants.
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.
Abdullah said he was "encouraged" by Trump's stated commitment to finding a solution to the decades-long conflict, which he said was a "potential major source of instability".
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