Somalis say that Bin Laden is innocent
The European Union withdrew its expatriate staff last week because of "general tension and uncertainty there" following the attacks on the US.
Last week, Somalia's Transitional Government denied having any links with Bin Laden and said that it was ready to co-operate with the US in its fight against international terrorism in the wake of the attacks on New York and Washington.
Radical links
US intelligence sources have suggested that the man held responsible for the attacks could be heading for Somalia.
Diplomats in east Africa have said that some radical Islamic groups in Somalia may be linked to his al-Qaeda network.
45 UN staff have been flown to neighbouring Kenya until new insurance cover can be found but the UN says Somalia has not become any less safe than before.
"I would like to stress that this decision has nothing to do with the security situation in Somalia, which remains stable and unchanged," said UN Resident and Humanitarian Co-ordinator Randolph Kent in Nairobi.
Thousands of people from all corners of Mogadishu attended Sunday's demonstration including hundreds of women wearing Islamic headscarves.
Peace
Some carried placards and photos of Bin Laden, the man the US believes to have been behind the attacks on the World Trade Center and the Pentagon.
The Transitional National Government earlier came out against the demonstration but did nothing to stop it going ahead for fear of provoking violence.
Sheikh Mohamud Sheikh Ibrahim Suley, one of the main organisers of the demonstration, told the BBC that the aim was not to support a man, but to stand up to international threats against Islam.
Burning flags
Many people waved pictures of Bin Laden in the air and buses are also displaying his photo in their windows with the caption: "Osama Bin Laden, the Hero of Islam."
At the end of the demonstrations, angry people set fire to the flags of the United States and Israel.
It has been suggested that Bin Laden would like to go to Somalia - the scene of the biggest US military defeat since Vietnam.
In 1995, the US cut short its intervention there intended to end the civil war and distribute food aid, after its troops suffered higher than expected casualties.
However, it is not clear how Bin Laden, believed to be in Afghanistan, would travel to Somalia without being intercepted by the US.