Libya has made several arrests in connection with the attack on the US consulate in Benghazi in which Ambassador Christopher Stevens was killed.
New Libyan Prime Minister Mustafa Abu Shaqur said the investigation was making progress.
The attack happened on Tuesday during protests over a US-made film that mocks the Prophet Mohammed.
Similar protests have spread across the Middle East and North Africa. Further unrest is expected at Friday prayers.
Clashes between riot police and protesters continued overnight in the Egyptian capital Cairo, where Islamist groups and others have called for a peaceful “million-man march” later on Friday.
US President Barack Obama has promised to do whatever is necessary to protect US citizens abroad and said he was urging foreign governments to guarantee their security.
A White House statement said he had thanked Yemeni President Abd-Rabbu Mansour Hadi for condemning an attack on the US embassy there and for launching an investigation.
“President Obama expressed appreciation for the co-operation we have received from the Yemeni government and underscored the importance of working together to ensure the security of US personnel,” the statement said.
In Benghazi, US and Libyan officials are investigating the possibility that heavily armed militants used the protest as a pretext for a co-ordinated assault.
Libyan officials say those arrested are being interrogated on suspicion of having instigated the attack.
Four embassy staff died, including Ambassador Christopher Stevens.
PM Mustafa Abu Shaqur blamed the attack on “criminals” and said anger against the film could not justify it.
“The people, they don’t understand that such a case like this, the American government has nothing to do with it,” he said.
“Somebody made a film and they put it on YouTube. It was very offensive for sure but that doesn’t justify taking this wild actions against Americans or American embassies. People can come out and demonstrate and express their opinion peacefully.”
Following the attack, some Libyans have taken part in rallies in Benghazi and Tripoli denouncing the violence.
Libyan Deputy Interior Minister Wanis al-Sharif told reporters that those arrested had been taken from their homes on Thursday but gave no further details.
No group has said it carried out the attack and Wanis al-Sharif said it was too early to say if those arrested belonged to a particular organization.
Meanwhile, further protests against the US-made film are expected on Friday.
In Yemen, demonstrators briefly stormed the grounds of the US embassy in Sanaa on Thursday and burnt the US flag before being driven back by security forces.
A White House spokesman said all those working in the embassy were safe and accounted for.
In Egypt, 224 people were injured in protests outside the US embassy in Cairo on Thursday, with some demonstrators demanding the expulsion of the ambassador. Police vehicles were set alight.
Egyptian media said that as night fell on Thursday, police were continuing to fire tear gas at stone-throwing protesters.
Calls for a million-man march in Cairo came from The Muslim Brotherhood, the Salafist al-Nour party and non-religious groups including the “Ultra” fans of Zamalek football club.
They said they had invited Muslims, Coptic Christians and all Egyptian citizens to join them.
President Mohammed Mursi said Egyptians rejected “any kind of assault or insult” against the Prophet Muhammad, but appealed for calm.
Small protests have also been reported in Bangladesh, Iraq, Morocco, Sudan and Tunisia, and security has been increased at US embassies and consulates around the world.
US Secretary of State Hillary Clinton has condemned the film, entitled Innocence of Muslims, as “disgusting” and “reprehensible” but said it was no excuse for violence.
The film was shot in the US and posted online earlier this year. It depicts the Prophet Muhammad as a womanizer and the bloodthirsty leader of a ragtag group of men who enjoy killing.
However, the film’s exact origin and the motivation behind its production remain a mystery.
Some of the actors involved have since condemned the film, saying they had no idea it was to be used as anti-Islam propaganda.