The four - including two Kenyans - were arrested last month with 98 packets of suspected heroin, with the US issuing an Interpol "red notice" for their capture and request for their extradition.
They are accused of orchestrating large scale shipments of heroin weighing several hundred kilo grammes, drugs worth hundreds of thousands of dollars.
Each was released on a cash bail of USD 55,000 and made to surrender their passports, magistrate Maxwell Gicheru said.
Their wealthy father, Ibrahim Akasha, was gunned down in Amsterdam in 2000, after fleeing Kenya where he was sought in connection with the seizure of several tonnes of hashish.
The two other suspects are Vijaygiri Anandgiri Goswami, an Indian, and Kulam Hussein, from Pakistan.
Magistrate Gicheru last month said that Kenya should cooperate with the extradition request "because international crime has hurt" the country.
With drug smuggling routes from Asia through the Middle East hampered by conflict and tougher border restrictions, traffickers have increasingly turned to east Africa as a transport hub, according to the United Nations Office on Drugs and Crime (UNODOC).
In April, British and Australian navies seized the largest ever haul of heroin at sea, weighing 1,032 kilo grammes.
The drugs, worth some USD 235 million (170 million were found on a dhow some 50 kilometers off the coast of Kenya and Tanzania.
East Africa has a small but growing domestic market for heroin, but the vast majority shipped to Kenya and Tanzania is believed to be then moved onwards to South Africa and west Africa, and potentially on to Europe.
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