The decision comes amid strain between the allies after NC denied Congress a Rajya Sabha seat; polls for four Upper House seats are due October 24.
NC vice-president Omar Abdullah said the party was open to supporting Congress if it had a stronger candidate for Nagrota.
The BJP has fielded Devyani Rana, daughter of late MLA Devender Singh Rana, who had won the seat in 2024 by a record margin.