A Bench headed by Justice DY Chandrachud refused to interfere in the High Court order.
Rai had won last year's Lok Sabha election from Ghosi parliamentary constituency in Mau, Uttar Pradesh, and has been in jail after an FIR was registered against him in a rape case.
The victim had challenged the High Court's January 23, 2020 order which has given two days custody parole to Atul Rai to take oath as MP on January 31.
Last year in May, a complaint was filed alleging rape and fraud against Rai at the Lanka police station in Varanasi.
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