Gates, the senior U.S. defense official, arrived in Riyadh on Tuesday afternoon following morning meetings in Cairo with Egyptian President Hosni Mubarak and Defense Minister Hussein Tantawi.
Gates was in the Mideast as Pakistan and Afghanistan's leaders arrived in Washington to meet with U.S. President Barack Obama. The defense secretary echoed the Obama administration's goal of enlisting both South Asian nations as full-fledged U.S. allies in the fight against the region's militants.
"My hope is, during the talks in Washington over the next few days, that there will be a common agreement on the nature of the threat, and the importance of Afghanistan and Pakistan working closely together with the United States and our partners to try and deal with that threat," Gates said.
He said the Taliban's recent attacks in Buner - about 60 miles outside Islamabad - "perhaps served as a wake-up call to many in Pakistan."
"Their response in sending the (Pakistani) army into Buner is a recognition of that threat," Gates said.
Gates also tried to tamp down Mideast concerns about American efforts to reconcile with Iran. He tried to reassure American allies Tuesday that there is no "grand bargain" in the works.
It's not clear any progress will be made, Gates said, because recent rhetoric from Tehran has been "not very encouraging."
At a press conference before leaving Egypt, Gates dismissed suggestions of any trade-off between the U.S. and Iran. He also pledged the U.S. will keep its allies in the loop as it reaches out to Tehran.
"The United States will be very open and transparent about these contacts, and we will keep our friends informed of what is going on so nobody gets surprised," Gates said.
He added: "One of the areas where I think there has been some exaggerated concern is some notion here in the region that there might be some grand bargain between the United States and Iran that would suddenly be sprung on them. I believe that kind of prospect is very remote."
Gates did not cite any specific concerns by Mideast allies, and an aide later said he generally uses the term "grand bargain" to define sweeping agreements to settle all outstanding diplomatic issues between nations.
But there has been widespread speculation in the region that the Obama administration would ask Israel to ease its demands during peace negotiations with the Palestinians in exchange for Tehran ratcheting back its nuclear weapons program.
Such a move would help bolster Iran's influence with the Palestinians at a time when it is trying to gain allies in the Arab world.
Neither Mubarak nor Tantawi was available to reporters before or after their closed-door meetings with Gates.
Gates left Cairo shortly after seeing Mubarak and headed to Riyadh for meetings with Saudi Arabia's interior minister and military officials.
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