The Olympics remark referred to the Winter Games now being held in Sochi, Russia.
"I don't think any of us have any expectation that they are going to turn on a dime," the official conceded. He said the administration would not exclude the possibility of reaching "a humanitarian resolution" despite Russia's "sorry record" of vetoing U.N. sanction resolutions.
King Abdullah said one of his main concerns, "is the rise of extremism in Syria, the sectarian violence, and if we don't find a solution, the spillover in the region and the effect that will have."
The two leaders considered ways their countries could support what they described as the "moderate opposition" movement, the senior official said.
Elsewhere in the United States, Sen. John McCain, R-Arizona, said "failure is looming" in the U.N.-mediated peace talks.
McCain also criticized Russia.
"The entire strategy for success at Geneva now relies on Russia putting pressure on the Syrian government to engage in a serious and constructive way," McCain said. "Yet, Russia has recently prevented the passage of a much-needed U.N. resolution on bringing aid to desperate Syrian civilians and continues to provide the means by which President Bashar al-Assad carries out his assault on the Syrian people.
"Such actions indicate that the Russian government is simply not a partner for peace in Syria and cannot be relied on to help secure a successful outcome," McCain said.
In Syria, rebels posted a video on social media purporting to show small group of fighters planting explosives in a tunnel underneath what they claim is the Carlton Hotel in Aleppo. The Syrian Observatory for Human Rights said the hotel serves as an anti-insurgency headquarters for government security forces.
CNN could not independently confirm the video's authenticity.
"We are putting our last touches and doing some measuring so we can make sure that we are under the Carlton Hotel," a rebel says in Arabic. "We are going to add the explosives after we finish everything, and you are going to hear good news, Aleppo people."
The video then cuts to an outdoor scene where billowing smoke rises over buildings, an apparent indication that the hotel was blown up Saturday.
The Syrian government didn't immediately respond to the rebels' claims in the video.
The snail-paced peace talks, which started last month with Brahimi serving as an intermediary between the two delegations sitting in the same room, have failed to produce an agreement on a first step for resolving the conflict, which has dragged on for nearly three years.
More than 140,000 Syrians have died since March 2011, according to the Syrian Observatory for Human Rights, a London-based opposition group.
About half of them were civilians, and more than 7,000 were children and more than 5,000 were women, it said.
It put Syrian military losses at more than 30,000 and pro-regime elements at more than 20,000. Those figures do not include the 18,000 Syrians who were jailed and are missing, it said.
Relief for besieged city
Brahimi said he would consult next with U.N. Secretary-General Ban Ki-moon and called upon him to hold discussions with U.S. Secretary of State John Kerry and Russian Foreign Minster Sergey Lavrov.
Brahimi said he would also likely brief the permanent members of the U.N. Security Council, known as the P5 -- the United States, Russia, Britain, France and China -- and the full Security Council.
The talks' only sign of progress has been a cease-fire to allow some evacuations from and aid relief to the besieged city of Homs.
U.N. Emergency Relief Coordinator Valerie Amos said Friday that 1,400 people were evacuated from the Old City of Homs and 2,500 still there got relief supplies, but she lamented the bleak humanitarian situation that prevails throughout the country.
"The little that has been achieved in Homs," Brahimi said, has given the Syrian people hope that they might finally be "coming out of this horrible crisis they are in."