The US secretary of state has promised prompt action if allegations of desecration of the Koran at the Guantanamo Bay prison camp prove true.
Afghan protesters shouted "Death to America"
But Condoleezza Rice appealed to Muslims to resist calls for violence, after at least seven deaths in three days of protests in Afghanistan.
The US authorities say they are investigating the allegations.
Ms Rice said desecration was abhorrent and disrespect for the Koran would not be tolerated.
The Saudi government has voiced "deep indignation" at the reported desecration, in the first official reaction from an Arab state.
Riyadh said the inquiry should be rapid and, if the allegations are found to be true, measures should be taken to prevent it ever happening again.
Speaking before a Senate committee, Ms Rice urged Muslims in America and throughout the world to stop the violence.
"I am asking that all our friends around the world reject incitement to violence by those who would mischaracterise our intentions," she said.
"Appropriate action" would be taken if the allegations proved true, she added.
"Disrespect for the holy Koran is not now, nor has it ever been, nor will it ever be, tolerated by the United States," she said.
At least seven people have died and many more have been hurt in the last few days as hundreds rioted in Afghanistan.
The protests followed reports in Newsweek magazine that interrogators at the US Guantanamo Bay prison had flushed at least one copy of the Koran down a toilet.
President Hamid Karzai said the violence showed the inability of Afghan authorities to handle such protests.
Two United Nations guest houses were attacked in Jalalabad, as were shops and government buildings, and the offices of two international aid groups were destroyed.
Many foreign aid agency personnel are being pulled out too.
There were also reports of anti-US protests in the south-eastern city of Khost, and in Laghman province, where a demonstration was dispersed peacefully by police.
Hundreds of inmates are still being held at Guantanamo Bay
The protests spread on Thursday to Kabul, where demonstrators poured onto the streets chanting "Death to America".
BBC correspondents say many Afghans are angry at what they regard as heavy-handed tactics used by American forces in their country.
Aid agencies have also become a focus of resentment.
Insulting the Koran or the Prophet Muhammad is regarded as blasphemy and punishable by death in both Pakistan and Afghanistan.
The US is holding about 520 inmates at Guantanamo Bay, many of them al-Qaeda and Taleban suspects captured in Pakistan and Afghanistan following the 11 September 2001 attacks in the US and subsequent US-led invasion of Afghanistan.