Editor's note: Read a version of this story in Arabic.
(CNN) -- French authorities said Wednesday that they will not authorize weekend demonstrations in Paris as protests over an anti-Muslim video started to fade worldwide.
Prime Minister Jean-Marc Ayrault told radio station RTL that French police forces have been reinforced should protesters organize.
"There is no reason to bring conflicts in our country that do not concern France," he said.
Adding to the debate, the French satirical magazine Charlie Hebdo published cartoons featuring a figure resembling the Prophet Mohammed in an issue that hit newsstands Wednesday.
Any depiction of Islam's prophet is considered blasphemy by many Muslims.
Magazine director Stephane Charbonnier told CNN affiliate BFM-TV that his staff is trying "to comment (on) the news in a satirical way."
French authorities stationed extra police protection outside the magazine's offices in advance of publication.
The offices were attacked in November when the magazine was due to publish an issue with a cover appearing to make fun of Islamic law.
"In France, we always have the right to write and draw. And if some people are not happy with this, they can sue us, and we can defend ourselves. That's democracy," Charlie Hebdo journalist Laurent Leger said. "You don't throw bombs, you discuss, you debate. But you don't act violently. We have to stand and resist pressure from extremism."
A demonstration took place Wednesday in Tyre, Lebanon, organized by Hezbollah, which the United States labels as a terrorist group. At a similar protest Monday in Beirut, thousands took part, waving Hezbollah flags and yelling, "America is an enemy of God."
"You most dignified of messengers, we are here to honor you, our prophet Mohammed," they chanted.
The reaction to the video in neighboring Iraq "has been quite muted" compared with elsewhere in the region, the nominee to be the U.S. ambassador to Iraq said Wednesday.
"There have been demonstrations throughout the country, but they have been low-level, and there has been nothing that is specifically threatening," Robert Stephen Beecroft said at a Senate Foreign Relations Committee hearing in Washington.
"There have been statements highly critical of the film that is at issue and statements by some political leaders that they should examine their relationship with the United States because of this film. But on the whole, we get good cooperation," he said.
Due to recent events, officials have taken an even closer look at security and are working with Iraqi officials to ensure that U.S. personnel are "safe as can be on our terms," he said.
"Innocence of Muslims" was an obscure Internet video until September 11, when rioters, seizing on it, breached the U.S. Embassy in Cairo. Protesters also attacked the U.S. Consulate in Benghazi, Libya, killing U.S. Ambassador Chris Stevens and three other Americans.
"The Innocence of Muslims" mocks the Muslim Prophet Mohammed as a womanizer, child molester and killer.
Washington has made it clear that it did not sanction the film, although it was produced in the United States. A week of protests have rippled from Morocco to Malaysia, spurring U.S. officials to increase security at diplomatic missions and demand other governments to take action.
Libya has taken steps to arrest those responsible for last week's deadly consulate attack, bringing in dozens for questioning over the weekend, Libyan officials said.
The exact number of arrests was unclear. One Libyan official said those arrested included suspects from Mali and Algeria as well as al Qaeda sympathizers.
Secretary of State Hillary Clinton said Tuesday that FBI agents had arrived in Tripoli. They had delayed entering the country a few days while the situation remained especially volatile.
The United States is looking at security at all diplomatic posts and will augment it at specific locations if necessary, Clinton said.
CNN's Susannah Palk, Salma Abdelaziz, Karen Smith, Virginia Nicolaidis, Josh Levs and Pierre Meilhan contributed to this report.