CHICAGO (CBS) — A federal judge has declined city officials’ request to lift an injunction preventing the start of construction on the Lucas Museum, at least for now.

The city has asked for permission to begin work on the $400 million Lucas Museum of Narrative Art, warning that a delay in construction could put the entire project at risk, if filmmaker George Lucas decides to find another home for the project outside Chicago.

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The request came two weeks after U.S. District Judge John Darrah rejected the city’s request to dismiss a lawsuit filed by Friends of the Parks, seeking to prevent the museum from being built on the lakefront. Darrah has barred any construction from beginning while the lawsuit is pending.

At a court hearing on Wednesday, Darrah said he would rule on the city’s request to lift that injunction on April 21. However, he suggested the city and opponents of the museum plan negotiate preliminary steps the museum could take at a low cost, without making significant changes to the proposed site, while the lawsuit proceeds.

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Museum officials had hoped to begin work on the 300,000-square-foot facility this spring, but that is on hold while Friends of the Parks proceeds with a challenge claiming the lakefront property where it would be built is protected land that should not be used for a private facility.

Darrah warned city officials, if he does lift the injunction on construction of the Lucas Museum while the lawsuit proceeds, any work on the project would have to be undone if the Friends of the Parks ultimately prevail in having the project declared illegal.

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A city spokesperson said that cost would not be on Chicago taxpayers, as the museum is to be privately funded.