Ghazi Aridi, the information minister, said early on Monday, after a late Sunday emergency cabinet meeting, that the government had unanimously "rejected and condemned the acts of riots ... that harmed Lebanon's reputation and its civilised image and the noble aim of the demonstration".
"The cabinet apologises to Denmark," Aridi said.
The interior minister, who is responsible for the police force that failed to stop the protesters, submitted his resignation at the session.
The parliamentary opposition and even some cabinet colleagues of Hassan Sabeh, the interior minister, had demanded he step down, but the government appeared divided, saying it only "took note" of the resignation offer.
The government also called for a speedy investigation.
Almost 30 people were injured as furious crowds on Sunday stormed and set ablaze the building housing the Danish consulate, despite the presence of riot police who had initially used tear gas and batons to keep protesters at bay.
"I submitted my resignation to the government after criticisms were raised," Sabeh said after the cabinet meeting on Sunday.
He said he had refused to give security forces the order to fire on the protesters because "I did not want to be responsible for any carnage.
Rioters trashed the Danish
consulate and set it on fire
"Despite the intervention of more than 1000 members of the security forces, we were unable to impose order because of the determination of the protesters, who numbered several thousands."
The Lebanese violence erupted the day after a similar attack on the diplomatic missions of Denmark and Norway in neighbouring Syria.
The offending caricatures, which included depictions of the Muslim prophet as a knife-wielding bedouin and another as wearing a time bomb-shaped turban, have sparked widespread protests across the Muslim world.
Iraq's Transport Ministry meanwhile announced it had frozen contracts with Denmark and Norway in protest against cartoons published in the countries' newspapers.
"This decision was taken to protest the cartoons of the Prophet Muhammad and we will not accept any reconstruction money from Denmark or Norway," said a spokesman on behalf of Salam al-Malaki, the transport minister .
"This decision was taken to protest the cartoons of the Prophet Muhammad and we will not accept any reconstruction money from Denmark or Norway"
Spokesman for Iraqi Transport Minister Salam al-Malaki
The spokesman said he did not know the value of contracts between Iraq and Norway and Denmark, which has more than 500 troops in Iraq.
Anti-government groups in Iraq have threatened Denmark's troops and a patrol was shot at on Sunday in an attack the Danish army said may have been connected to the furore.
Per Stig Moeller, Denmark's foreign ministerm rejected that Danish contracts had been frozen.
"That is not the message we have been given by the Iraqi government," Moeller told Danish TV2 News.
But the anti-immigrant Danish People's Party (DPP), which the government relies on for support to maintain a majority but is not in government itself, said it was surprised at the Iraqi decision.
Soeren Espersen, the party's foreign policy spokesman, told Ritzau news agency: "If the Transport Ministry's decision reflects the position of the whole Iraqi government, it means that one of the key reasons for being in Iraq has disappeared."
"We spend a lot of resources rebuilding their land. I had expected Iraq to stay out of the Muhammad discussion," he said.
Call for attacks
Earlier on Sunday, more anti-US groups called for attacks on Danish troops in Iraq and people from all countries where cartoons of the Prophet Muhammad have been published.
In an internet statement, the Islamic Army in Iraq, which has claimed responsibility for killing foreign hostages, urged militants to kidnap Danes and "cut them into as many pieces as the number of newspapers that printed the cartoons".
Another group, the Mujahideen Army, called for attacks last week.
The Danish army said a patrol in southern Iraq was shot at on Sunday while it was giving first aid to a group of children after a traffic accident.
"This unusual attack against helpful Danish soldiers suggests that some Iraqis are carried away by the anger which has spread throughout most of the Middle East," the army said in a statement, adding the situation was more tense than normal.
A Roman Catholic priest has been shot dead on Sunday in the courtyard of a church in Turkey, amid fears the murder could be linked to the uproar over the cartoons.
Italian priest Andrea Santoro, 59, was shot twice in the entrance of the Santa Maria Catholic Church in the northern city of Trabzon after Sunday mass, with the Vatican ambassador to Turkey saying the armed man shouted "God is great" as he fired his pistol.
Turkey has condemned the
murder of the Christian priest
"We don't have much to go on to make a proper interpretation of what happened.
However, the only element which a collaborator of Father Santoro's mentioned to me is that the person who killed him shouted 'Allahu Akhbar'," Monsignor Antonio Lucibello was quoted by Italy's Ansa news agency.
"There are claims that the incident may be related to the cartoons," Huseyin Yavuzdemir, the governor of Trabzon, told Anatolia news agency. "This will become clear when the suspect is captured."
The Turkish government "ferociously" condemned the murder and promised to find the perpetrator, described by witnesses as a male in his late teens.
The Vatican embassy in Ankara said Santoro was originally from Piverno, a small town near Rome.
Yavuzdemir said the police obtained information the priest had been threatened by locals in the past over alleged efforts to convert Muslims, but there was no indication that the church was involved in missionary work.
"The security forces are investigating the people who have threatened and criticised him," Yavuzdemir said, adding that Santoro had not demanded protection from the police.
The Santa Maria Church in Trabzon, a port city on the Black Sea coast, was built in the second half of the 19th century on the orders of an Ottoman sultan to serve foreign visitors, according to the city's official website.