A judge will decide whether Asher Karni, 50, should be freed on $75,000 bail or remain in jail until his trial.
Kami was arrested on 2 January at Denver International Airport after he arrived for a ski holiday.
On Monday a US judge ordered him freed on a $75,000, provided he remained at his rabbi's home in Maryland while his case proceeds in Washington.
But Karni was not released immediately, pending an appeal by federal authorities in Washington who have until Thursday to ask the judge to keep him in custody.
The US government has charged Karni, who lives in South Africa, with conspiring to send and hide the identity of the "triggered spark gaps" headed for Pakistan.
A spark gap, which can send a synchronised electronic pulse to detonate a nuclear weapon, is also used by hospitals to destroy kidney stones. No special permission is needed if the devices are sent to a hospital.
But the US government said Karni falsely listed a hospital in South Africa as the receiver. If he had listed Pakistan as the destination, a special US export permit would have been needed.
According to a prosecution affidavit filed with the court, US authorities said Karni admitted the scheme to South African authorities who searched his business in Cape Town in December.
Court papers said Karni ordered the triggers, which are made by Perkin Elmer Optoelectronics of Massachusetts, through a New Jersey export company.
A shipment of 66 triggers, deliberately disabled by Perkin Elmer, was sent to Karni's South African company, the court records showed.
And an e-mail, purportedly from Karni to the New Jersey company, said he had forwarded the triggers to "the customer".