Speaking in Rabat, Morocco, where she inaugurated the new U.S. embassy, Clinton, in response to a reporter's question, said the United States is condemning the violence "in the strongest possible terms, but we also believe that the violence must stop and the hard work of trying to build a more peaceful, prosperous, secure Afghanistan must continue," a State Department transcript said.
Deadly protests that erupted last Monday after Afghans heard that NATO forces had accidentally burned some copies of the Muslim holy text have continued to spread despite apologies from NATO and the United States, including President Barack Obama.
More than 20 Afghans have died in the protests as well as four Americans. Two of the victims were senior U.S. military officers, who were killed inside the Afghan Interior Ministry by an Afghan intelligence worker in an act later claimed by the Taliban.
On Sunday, protesters in northern Kunduz province attacked the police chief's office and a U.S. military base. A Kunduz police spokesman told CNN the protesters threw a hand grenade at the base, injuring seven U.S. military personnel believed to be Special Forces members. Last week, two U.S. soldiers were killed at a military base by a man wearing an Afghan National Army uniform.
Clinton, speaking to CNN in an interview in Rabat, took issue with the criticism of President Obama's apology by Republican presidential candidates and some experts.
"I find it somewhat troubling that our politics would inflame such a dangerous situation in Afghanistan," Clinton was quoted as saying.
In his letter to Afghan President Hamid Karzai, Obama said the burning of the Koran was "inadvertent" and an "error."
"It was the right thing to do to have our president on record as saying this was not intentional; we deeply regret it," Clinton said.
"We are hoping that voices inside Afghanistan will join that of President Karzai and others in speaking out to try to calm the situation. It is out of hand and it needs to stop."