The call follows the fallout from the Trump administration's decision to recognise Jerusalem as Israel's capital.
Mr Pence, in turn, tried to reassure the monarch that the Trump administration remains committed to restarting Israeli-Palestinian peace efforts and views Jordan as a central player.
The vice president also said that "the United States of America remains committed, if the parties agree, to a two state solution".
Such a caveat deviates from long-standing US support for a two-state solution as the only possible outcome of any peace deal.
President Trump's pivot on Jerusalem last month infuriated the Palestinians, who seek the Israeli-annexed eastern sector of the city as a future capital.
They accused the US of siding with Israel and said Washington can no longer serve as a mediator.
Jerusalem is the emotional centrepiece of the long-running conflict, and President Trump's policy shift set off protests and condemnation across Arab and Muslim countries.
It posed a dilemma for King Abdullah, who is a staunch US ally, but also derives his political legitimacy in large part from the Hashemite dynasty's role as guardian of a key Muslim site in Jerusalem.
Any perceived threat to Muslim claims in the city is seen as a challenge to Jordan, where a large segment of the population is of Palestinian origin.
Mr Pence told Jordan's monarch that President Trump made it clear in his announcement on Jerusalem "that we are committed to continue to respect Jordan's role as the custodian of holy sites, that we take no position on boundaries and final status".
He said Jordan would continue to play a central role in any future peace efforts.
The vice president also praised Jordan's contribution to a US-led military campaign against Islamic State extremists who in recent months were pushed back from large areas in Iraq and Syria, both neighbours of Jordan.
King Abdullah expressed concerns about the regional fallout from the Jerusalem decision.
"Today we have a major challenge to overcome, especially with some of the rising frustrations," he said.
He described the Pence visit as a mission "to rebuild trust and confidence" in getting to a two-state solution, in which a state of Palestine would be established in the West Bank, Gaza Strip and east Jerusalem, lands Israel captured in 1967.
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