Nagar was suspended in October 2013 over allegations of rape against him.
"The suspension of Nagar from the party has been revoked as per the direction of the PCC (Pradesh Congress Committee) president Sachin Pilot," PCC vice president Archna Sharma said.
Nagar was food and civil supply minister in the Congress government led by Ashok Gehlot.
The bypolls in Ajmer and Alwar Lok Sabha constituencies and the Mandalgarh assembly constituency (Bhilwara district) will be held on January 29.
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