Police had banned the march which began after Muslim Friday prayers
At least five people have died after Kenyan police opened fire at supporters of a Jamaican-born Muslim cleric notorious for preaching racial hatred.
Police also fired tear gas at hundreds of stone-throwing protesters calling for Abdullah al-Faisal to be freed.
Faisal is in detention in Nairobi after Kenya failed to deport him.
Kenya wants to expel him citing his "terrorist history". He was jailed for four years in the UK for soliciting the murder of Jews and Hindus.
An unnamed senior police officer told the AFP news agency that five people had died, while one of the protest organisers told AP that seven people had lost their lives.
Sources at the Kenyatta Hospital have confirmed that one person has died, while seven others sustained bullet wounds. Doctors say their lives are not in danger.
At least four police officers have been hospitalised, AFP reports.
Muslim youths began the protest match after Friday prayers at the Jamia Mosque in the centre of Kenya's capital, Nairobi.
FAISAL'S STORY SO FAR...
11 January: Nigeria returns him to Kenya
7 January: Kenya says he has been sent to The Gambia
5 January: Kenya says he has been sent to Tanzania
31 December 2009: Arrested
24 December: Enters Kenya
2007: Deported from UK
2003: Jailed in UK for preaching racial hatred
They wanted to present a petition to Immigration Minister Otieno Kajwang and Prime Minister Raila Odinga's office.
But police had banned the march and intervened.
One banner read: "Release al-Faisal, he is innocent", reports the AFP news agency.
Reuters news agency reports that some people joined the security forces in attacking the protesters.
Faisal was arrested on 31 December 2009, a week after he is believed to have arrived from Tanzania.
Mr Kajwang says The Gambia has agreed to take him in but Kenya was unable to send him there because airlines in Nigeria refused to carry him.
Tanzania has also refused to let him re-enter its territory.
Faisal was born Trevor William Forrest in St James, Jamaica - though he left the island 26 years ago, initially living in the UK.
His parents were Salvation Army officers and he was raised as a Christian.
But at the age of 16 he went to Saudi Arabia - where he is believed to have spent eight years - and became a Muslim.
He took a degree in Islamic Studies in the Saudi capital of Riyadh, before coming back to the UK.
Faisal spent years travelling the UK preaching racial hatred urging his audience to kill Jews, Hindus and Westerners.
A year after being deported from the UK in 2007, he was preaching in South Africa.
The Kenyan authorities said Faisal had arrived in Kenya on 24 December 2009 after travelling through Nigeria, Angola, Mozambique, Swaziland and Malawi and Tanzania.