Some lawmakers in the House introduced the bill in June.
The House of Representatives has rejected a bill seeking a six-year single term for Nigeria's presidency.
The constitution alteration bill, sponsored by Ikenga Ugochinyere (PDP, Imo) and 33 others, was rejected on Thursday during a debate on its general principles.
Some lawmakers in the House, who introduced the bill in June, also proposed rotating the presidency between the North and the South and creating a second vice president.
In addition, the bill sought to amend the Constitution to create the offices of two vice presidents from the southern and northern parts of Nigeria. The 1st Vice President shall be a succession vice president, while the 2nd Vice President shall be a minister in charge of the economy. Both vice presidents shall be ministers.
The bill also proposed that the President and the 1st Vice President shall come from the same part of the country (North or South), and the 1st Vice President shall become President whenever the President becomes incapacitated, i.e., V.P. (Succession), V.P. (Administration and Economy)
Rejection of the bill
During the plenary, Mr Ugochinyere's colleagues did not allow him to lead the debate on the bill before rejecting it.
He had moved a motion to read the bill for a second time, but when Speaker Abbas Tajudeen put it to vote, members overwhelmingly voted against it.
Atiku's support for the bill
Former Vice President Atiku Abubakar backed some of the proposals in the now-rejected bill, notably the rotation of the presidency among the six geopolitical zones and a single six-year term.
In August, Atiku sent a memo to the Deputy Senate President, Barau Jibrin, who also chairs the Senate Committee on Constitution Review.
The 2014 National Conference also recommended a similar power rotation: the governorship seat should rotate among the three senatorial districts in each of the 36 states.
The then administration of President Goodluck Jonathan did not implement the conference's recommendations before it left office.