To cheers from opponents, Senate President Ken Nnamani ruled that the voice vote had defeated the measure introduced by Obasanjo's allies and that "the Senate has said clearly and eloquently that we should discontinue other proceedings on this amendment."
The proposed amendment needed to pass by a two-thirds margin in Nigeria's federal and regional parliaments. Tuesday's floor vote in the capital, Abuja, appeared to cripple the drive by Obasanjo's supporters.
Obasanjo hasn't said publicly whether he would run for a third term, but has indicated he would like to see through wide-ranging reforms he implemented after his first election in 1999 cemented the end of brutal military rule.
His supporters have rejected charges the third-term drive was undemocratic and could open the way to dictatorship, saying Nigerians would still choose their president at the ballot box, the AP reports.
For weeks, some senators have been alleging that some have been offered and others have accepted bribes up to 50 million naira (US$358,000; about Ђ280,000) to persuade them to vote for the constitutional amendments.
The FSB of Russia has distributed the footage of video surveillance over suspects, who allegedly worked to orchestrate a military coup in Belarus and planned to assassinate its president, Alexander Lukashenko