"I am very concerned about Syria becoming an enclave for extremism," Obama said, adding that extremism thrives in chaos and failed states. He said the rest of the world has a huge stake in ensuring that a functioning Syria emerges.
"The outcome in Syria is not going to be ideal," he acknowledged, adding that strengthening a credible opposition is crucial to minimizing the difficulties.
Eager to resolve another source of tension in the region, the president earlier Friday helped broker a phone call between the Israeli and Turkish prime ministers that led to the restoration of normal diplomatic relations between the two countries.
While Obama was in Israel, Netanyahu placed a call to Turkey's Recep Tayyip Erdogan to apologize for the deaths of nine Turkish activists in a 2010 Israeli naval raid on a Gaza-bound international flotilla.
"The timing was good for that conversation to take place," Obama said.
Obama, at a joint news conference with Abdullah, said his administration is working with Congress to provide Jordan with an additional $200 million in aid this year to cope with the massive influx of refugees streaming across the border from Syria.
Abdullah said the refugee population in his country has topped 460,000 and is likely to double by the end of the year -- the equivalent of 30 million refugees in the United States, he said.
Obama also said he would "keep on plugging away" in hopes of getting the Israelis and Palestinians to reach a peace agreement.
"The window of opportunity still exists, but it's getting more and more difficult," the president said. "The mistrust is building instead of ebbing."
On Iran, Obama reiterated that the United States is open to "every option that's available" to keep the country from developing a nuclear weapon.
He said it would be "extraordinarily dangerous" for the world if Iran does become nuclear capable, and he expressed his desire for using diplomatic means to halt Iran's nuclear aspirations.
Iran insists its nuclear program is for peaceful purposes.
"My hope and expectation is that, among a menu of options, the option that involves negotiations, discussions, compromise and resolution of the problem is the one that's exercised," Obama said, "but as president of the United States I would never take any option off the table."
Obama arrived in Jordan Friday evening, the final stop on a four-day visit to the Middle East that included his first stop in Israel as president.
He began his visit to Amman with an apology.
"I apologize for the delay," Obama told Abdullah after arriving about an hour behind schedule. "We ended up having a dust storm."
The two leaders headed to dinner after their news conference. On Saturday, Obama plans several hours of sightseeing, including a tour of the fabled ancient city of Petra, before the return trip to Washington.