Abdullah and his wife, Queen Rania, called on the pope on Monday at his papal summer residence in Castel Gandolfo, south of Rome.
In a letter published on Monday in the Corriere della Sera newspaper, Abdullah called for the world to reject attempts by extremists to create a clash of civilisations between Islam and the West.
He said such a clash weakens efforts to bring peace and prosperity to the world.
"All of us must assume the responsibility to refute hatred, ignorance and violence," he wrote. "This requires an honest and continuous dialogue between the West and the Islamic world."
He said his audience with the pope was part of that effort and "will take forward a positive and respectful confrontation between our two faiths". Benedict has echoed similar themes in his comments about terrorism and relations with Muslims.
During his meeting with Muslim leaders last month in Cologne, Germany, the pope invited Muslims to join Christians in trying to combat the spread of terrorism and "turn back the wave of cruel fanaticism" behind it.
"Those who instigate and plan these attacks evidently wish to poison our relations, making use of all means, including religion, to oppose every attempt to build a peaceful, fair and serene life together," Benedict said.
Benedict had been cautious about making any links between terrorism and Islam, rejecting the idea that the world faced a "clash of civilisations".
But in warning that the world risked exposure to "the darkness of a new barbarism", Benedict stressed that Muslim leaders must "guide Muslim believers and train them in the Islamic faith".