"Over the weekend, I was approached by the All India Tennis Association with a request to pair with Leander Paes as the AITA's 'second choice' team," Bopanna said in a statement.
"With all respect and humility, I have been unable to accept AITA's offer and have communicated my decision to them in writing this morning," he said.
Bhupathi, who has threatened to skip the Games rather then partnering Paes, and Bopanna maintain they have qualified for London as a partnership based on their rankings and should not be separated.
AITA must find another partner for Paes, whose top-10 ranking gives him direct entry, they say.
"Since the beginning of the year, I have partnered with Mahesh Bhupathi towards playing together as a team at the Olympics. This was communicated to the AITA at every step and we were encouraged to continue to play together," Bopanna said.
"Having played alongside Leander Paes only twice during my career, I recognise that as a team we are underprepared for the demands of the Olympics and ... I could not accept AITA's offer that we play together," he added.
The pressure on AITA increased with sports minister Ajay Maken also questioning the logic behind fielding one team in London.
"We can send 2 teams, why send 1?" Maken wrote on his Twitter page.
There is also uncertainty over which mixed doubles team India will field in London.
Sania Mirza and Bhupathi won the French Open mixed title earlier this month but so far it has yet to be confirmed who will partner Mirza in London.
"Hidden question is on who should pair Sania? Why disturb victorious grand slam mixed double pair?" Maken asked.
AITA chief Anil Khanna, who maintained that India's best chance of winning a tennis medal in London was through the Paes-Bhupathi partnership, was not available for comment.
Paes has said he was ready to team up with whoever AITA selected.
Winner of the singles bronze at the 1996 Atlanta Olympics, Paes joined hands with Bhupathi to form a formidable partnership in the late 1990s, winning three grand slams.
However, the ageing duo are not even on speaking terms after a second acrimonious split last year.