Abdullah told Pence their discussions would be "candid and frank" as they met at his palace in the Jordanian capital, Amman, during the second stop of the vice president's peace mission to the Middle East.
"I had continuously voiced over the past year, in my meetings with Washington, my concerns regarding the U.S. decision on Jerusalem that does not come as a result of a comprehensive settlement to the Palestinian-Israeli conflict," Abdullah said. "Today, we have a major challenge to overcome, especially with some of the rising frustrations."
He added it is "very important" to find a way to move forward with a two-state solution in the conflict between Israel and the Palestinian state in what he described as "a very critical point" for the region.
Pence reaffirmed President Donald Trump's decision to name Jerusalem the capital of Israel and move the U.S. embassy from Tel Aviv to Jerusalem, while adding the United States is committed to achieving peace between the two sides.
"President Trump made a historic decision to recognize Jerusalem as the capital of Israel. But as he also made clear in that decision, the United States of America remains committed, if the parties agree, to a two-state solution. We are committed to restarting the peace process," said Pence.
Before arriving in Jordan, Pence visited Cairo where he promised the United States will continue to support Egypt's battle against terrorism.
The vice president will fly to Israel Sunday evening where he will address the Knesset -- Israel's parliament -- and meet with Israeli Prime Minister Benjamin Netanyahu.
Some Knesset members have planned to disrupt Pence's visit, an act Netanyahu called a "disgrace."
"We will all be there and share the great honor that he deserves," he said.
Netanyahu referred to Pence as a "great and true friend of Israel" and said they planned to discuss "Trump's efforts to curb Iranian aggression and the Iranian nuclear program," as well as peace and security.
"Those who truly aspire to these goals know that there is no substitute for the leadership of the United States," said Netanyahu.