Rahat, along with two of his colleagues Maroof and event manager Chitresh Shirivastava, has been asked to appear before the Directorate of Revenue Intelligence (DIR) Feb 17, informed sources said.
The three were asked by the DRI to surrender their passports and appear again for questioning in three days.
Rahat was released after an assurance by the Pakistan high commission that he will cooperate with the probe, the sources added. He has been told not to leave the country.
"We are only questioning him. We will be shortly taking a decision, " Vijaylakshmi Sharma, director-general of the DRI, told reporters when asked about the outcome of the interrogation.
Rahat was detained at New Delhi's Indira Gandhi International Airport Sunday on his way back to Pakistan after attending concerts and award functions in India.
"The DRI officers found altogether $124, 000, which is equivalent to about Rs.60 lakh. $24, 000 were found from the baggage carried by Rahat while the remaining $50, 000 each were found from the baggage of two troupe members, " Central Board of Excise and Customs chairman S. Dutt Majumdar said.
Majumadar added that there were "clear violations of excise laws" and the currency carried by them was "much above" the allowed limit.
According to norms, no one can carry beyond $5, 000 in cash and $5, 000 in other instruments. The person has to declare to the Customs Department if he is carrying more than this amount.
Islamabad started working up diplomatic channels to free Rahat Ali after he was detained Sunday night.
Government sources in New Delhi Monday said India's external affairs ministry has been in touch with Pakistan's Foreign Office over the issue.
Three officials from Pakistan's high commission in New Delhi came to zonal headquarters of the DRI where the singer was interrogated, but left after about 30 minutes, the sources said.
Pakistan's Foreign Secretary Salman Bashir called India's High Commissioner Sharat Sabharwal in Islamabad and discussed the matter around midnight Sunday. He requested the Indian envoy to ensure that "no official should misbehave with Rahat during interrogation".
Bashir also called up Pakistan's High Commissioner to India Shahid Malik and directed him to "take immediate steps for securing release of Rahat".
"The matter should be taken up formally with the Indian foreign office, " he said, adding that "contact with Indian authorities for updates in the case must be maintained throughout".
Malik spoke with Vivek Katju, Secretary (West) in India's external affairs ministry, insisting that the protective custody of the singer be lifted, Pakistan's state-run APP news agency quoted a statement from the Pakistan Foreign Office as saying.
Earlier, Pakistan's Interior Minister Rehman Malik called Shahid Malik and directed him "to provide necessary legal and other consular help to Rahat".
Rahat's brother-in-law, Asim Raza, told Dunya TV that they "received information from the media and were feeling concerned about it". "We are yet to establish any proper contact with the authorities in India although Rahat talked briefly with his wife and asked her to remain hopeful of a positive outcome".
Rahat, the nephew of legendary singer Nusrat Fateh Ali Khan, is popular both in India and Pakistan. Several of his hit songs from Indian films are a rage on both sides of the border, for which he has won several awards, including the recent Filmfare award for "Dil to Bacha Hai Ji".