The legal challenge to the eviction was filed by local lobby group the Centre for Policy Alternatives.
The court set the first formal hearing for July 26, without explaining the delay, but kept a ban on security forces repeating a recent operation in which nearly 400 Tamil men, women and children were taken out of the capital by bus.
"The case was fixed for July 26, when all sides have been asked to support the issues they are canvassing," a court official said following a preliminary hearing.
Sri Lanka's government came in for heavy criticism for the operation two weeks ago, with rights groups saying the eviction of Tamils was a form of "collective punishment.
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The government apologised, although police argued that Tamil Tiger suicide bombers and assassins had been using low-budget accommodation in Colombo to plan attacks.
The Supreme Court's intervention followed a complaint by a political lobby group that the police swoop, in which hundreds of Tamils were dragged out in their n