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Mr. Kerry has sought to enlist Russia's cooperation for a political solution to the war in Syria and met last week with Foreign Minister Sergey V. Lavrov.

But Mr. Kerry said in Riyadh that Russia has continued to send weapons to forces loyal to Mr. Assad.

"Believe me, the bad actors, regrettably, have no shortage of their ability to get arms — from Iran, from Hezbollah, from Russia, unfortunately," Mr. Kerry said in a joint news conference with the Saudi foreign minister, Prince Saud al-Faisal.

Mr. Kerry attended an international conference in Rome last week that was convened to show backing for the Syrian opposition.  The secretary of state appeared to welcome some outside efforts to provide military support to rebels in Syria, even though the Obama administration has decided not to send arms. Asked if there was a danger that arms sent by Saudi Arabia might fall into the wrong hands, Mr. Kerry said that it was important to put pressure on the Assad government.

"There is no guarantee that one weapon or another might not, at some point in time, flow into the wrong hands," he said. "But I will tell you this: there is a very clear ability now in the Syrian opposition to make certain that what goes to the moderate, legitimate opposition is in fact getting to them and the indication is that they are increasing their pressure as a result of that. "

"Morally, we have a duty," said the Saudi foreign minister, alluding to efforts to provide military support.

He added that the Assad regime was firing missiles at population centers in Syria at times of the day when civilians were concentrated. "Nobody who has done that to his citizens can claim a right to lead a country," he said.

While it has decided not to send arms, the Obama administration said that it will send food and medical supplies to the armed wing of the Syrian opposition. Britain is expected to soon announce a package of nonlethal military assistance, such as vehicles.

Mr. Kerry had a working lunch on Monday with Mahmoud Abbas, the president of the Palestinian Authority, who was visiting Riyadh along with leaders from the Gulf states. The meeting comes two weeks before President Obama and Mr. Kerry are planning to travel to Israel, Palestinian areas and Jordon to hear ideas for trying to revive the Middle East peace effort.

On Iran, Mr. Kerry repeated the American refrain that time was running out for a diplomatic solution regarding Iran's refusal to accept internationally verified limits on its nuclear program. He reiterated  the argument that allowing Iran to develop nuclear weapons would encourage nuclear proliferation and heighten tensions in the region.

"But talks will not go on for the sake of talks, and talks cannot become an instrument of delay that will make the situation more dangerous," Mr. Kerry said. "So there is a finite amount of time."

Saudi Arabia was the seventh stop on Mr. Kerry's nine-nation tour. His next are the United Arab Emirates and Qatar, nations that are very concerned about Iran and the situation in Syria.