Hawit, 64, who was extradited to the United States on Wednesday from Switzerland following his arrest on December 3, denies 12 charges including racketeering conspiracy, wire fraud and money laundering.
Attorney Justin Weddle requested to judge Robert Levy that Hawit should be allowed to be placed under house arrest and fitted with an electronic monitoring device at his daughter's home in Miami.
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Levy rejected the request but left the open the possibility the court could reconsider if Hawit deposited a "significant amount" of around $20,000-$50,000.
Prosecutors have described Hawit as a significant flight risk and demanded that bail be posted at $4 million -- guaranteed by either $500,000 in cash or US property.
Hawit, the suspended head of CONCACAF, the regional body for football in North and Central America and the Caribbean, is one of 39 officials and marketing executives accused of soliciting and receiving tens of millions of dollars in bribes and kickbacks.
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US prosecutors allege that Hawit accepted and laundered hundreds of thousands of dollars in bribes as general secretary of the Honduran soccer federation between 2008 and 2014.
Swiss authorities announced on January 6 that he had agreed to be sent to the United States.
Hawit is the fifth FIFA official extradited by Switzerland to the United States in connection with the deepening multi-million-dollar corruption scandal that has rocked world soccer since May.
A further hearing has been set for January 21.
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