(Updates with background)

NAJAF, Iraq, March 29 (Reuters) - Shi'ite cleric Moqtada al-Sadr has told his followers not to lay down their arms, rejecting a demand by the Iraqi government which launched a crackdown against them this week, a top aide said on Saturday.

"Moqtada al-Sadr asks his followers not to deliver weapons to the government. Weapons should be turned over only to a government which can expel the occupiers," aide Hassan Zargani told Reuters by telephone.

A member of the Sadrist political committee in the holy Shi'ite city of Najaf, Haidar al-Jabari, confirmed the remarks.

Iraqi security forces launched an offensive against Mehdi Army fighters loyal to Sadr in the southern oil port of Basra but have so far failed to dislodge the militants from their strongholds.

Fighting has since spread to other towns and cities in southern Iraq where the Medhi Army has a presence.

Prime Minister Nuri al-Maliki has given Shi'ite militants in Basra until April 8 to surrender their weapons. Mehdi Army fighters in the city have rejected the ultimatum.

(Reporting by Khaled Farhan; writing by Peter Graff; editing by Jon Boyle)

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