Central ministers Mukhtar Abbas Naqvi and RCP Singh resigned on Wednesday, a day before the end of their Rajya Sabha term.
Prime Minister Narendra Modi praised both Mr Naqvi and Mr Singh as they attended their last cabinet meeting this morning.
The Rajya Sabha terms of Minority Affairs Minister Mukhtar Abbas Naqvi and Steel Minister RCP Singh end on Thursday. The BJP didn't renominate Mr Naqvi and Mr Singh, Bihar Chief Minister chief Nitish Kumar's one-time confidante and No. 2 in the party, failed to get another Rajya Sabha term as his party boss was reportedly not happy with his proximity to senior partner BJP.
There is speculation that Mr Naqvi, 64, may be chosen by the BJP as its candidate for Vice President of India. Mr Naqvi met with BJP president JP Nadda before handing in his resignation to PM Modi, fueling more talk.
Apart from Union Defence Minister Rajnath Singh, Mr Naqvi was the only other minister who was also in the Atal Bihari Vajpayee led-BJP government.
The ruling party has been discussing a representative of a minority community for the second highest constitutional post, especially at a time the BJP is facing an unprecedented backlash over the Prophet Muhammad comments by suspended spokesperson Nupur Sharma.
M Venkaiah Naidu's term as Vice President ends on August 10.
July 19 is the last date for nominations for Vice President. The elections will be held on August 6.
Kerala Governor Arif Mohammad Khan, former Union Minister Najma Heptulla and former Punjab Chief Minister Amarinder Singh are also in the running, reports say.
The BJP has named Droupadi Murmu, a tribal leader from Odisha, as its presidential candidate.
The party has enough numbers to have its candidates elected to the two posts.