Hamas "is prepared to play a role in calming the situation between the Islamic world and Western countries on condition that these countries commit themselves to putting an end to attacks against the feelings of Muslims", the organisation's leader Khaled Meshaal told a news conference in Doha on Thursday.
His conciliatory tone came a day after he warned the Western press was "playing with fire" by publishing the cartoons which have led to riots around the world.
A senior figure at Al-Azhar, the highest authority in Sunni Islam, said it was time to move on from high emotion to constructive dialogue.
"Quiet debate and dialogue, without passion" is the way forward, Ali al-Samman, who heads an interconfessional dialogue committee at the prestigious seat of learning in the Egyptian capital, said.
As Muslim protests over the cartoons subsided on Thursday, a Taliban commander in Afghanistan warned that 100 fighters had enlisted as suicide bombers and Denmark said it feared for the safety of its troops in Iraq.
Mullah Dadullah, one of the Taliban's most senior military commanders, said his group had also offered a reward of 100kg of gold to anyone who killed people responsible for the drawings.
Meanwhile Afghan authorities arrested more than 40 Pakistani workers for inciting violence on Wednesday during a protest against the cartoons in which four people were killed.
The deaths in Qalat raised the death toll to 11 in five days of protests in Afghanistan against the cartoons. Two people have also died in protests in Somalia and Lebanon.
Protests against the EU broke
out in the Palestinian territories
The cartoons were first published in the Danish daily Jyllands-Posten in September, but have since been widely reprinted.
The newspaper's chief editor, Carsten Juste, said on Thursday the culture editor who had decided to publish the cartoons, Flemming Rose, had been sent on holiday for an indefinite period "because nobody can bear the weight that is on his shoulders", according to the online edition of the Danish daily Politiken.
However, Most Danes hold Muslim religious leaders responsible for the furore over the cartoons, according to a poll published in Denmark on Thursday.
A total of 58% of respondents to the tMegafon poll blamed the imams while 22% placed the responsibility on the Jyllands-Posten daily.
A further 11% put the blame on Middle East governments.
Separately, Denmark's biggest tour operator, Star Tour, said it had scrapped all its trips to Egypt and Morocco until April due to mass cancellations over fears of violence related to the cartoon row.
In Paris, close to 100 Arab and European academics, political
and religious figures also issued a joint appeal for "moderation and wisdom" in the row.
However in Lebanon, the head of the country's Shia movement Hizb Allah insisted on an apology for the cartoons, as hundreds of thousands of Shias gathered in southern Beirut to mark the Ashura festival.
Lebanon's Hizb Allah ruled out a
compromise without an apology
"There will be no compromise before we receive an apology," Hassan Nasrallah told the crowds at the Shia gathering.
Also on Thursday, up to 15,000 South African Muslims also took to the streets in Cape Town, and handed over a petition to the Danish consulate.
The US warned of potential violence during protests planned this week in Kenya's capital. Kenyan Muslims have called for demonstrations, including a possible march on the Danish embassy in Nairobi.
Egyptian writer and Nobel literature prize laureate Naguib Mahfouz said a boycott of Danish products was "the only option" for Muslims to retaliate.
A boycott of Danish goods in Muslim countries in reaction to he cartoons has been gaining ground, with the EU threatening retaliatory action against countries involved.