"The coalition rejects the elections so far conducted and demands for an indefinite postponement of further elections until a structure that guarantees transparency and fairness of the electoral process can be established," the coalition said in a statement.
The group includes former army ruler Muhammadu Buhari and vice-president Atiku Abukar, the two main challengers to the ruling party.
"The coalition calls on Nigerians to protest in a non-violent manner the sham elections so far conducted."
It also called on the National Assembly to reconvene immediately "to make resolutions confirming the illegitimacy of elections so far conducted".
But Obasanjo, in an interview with the Financial Times published on Wednesday, appeared unfazed despite the chaotic elections.
"I won't say I am absolutely unconcerned, but I'm not concerned to the point that I would say that we haven't had a reasonable and fairly good election," he said.
He said there had been improvements in the conduct of polls, highlighting that voter registration had been done electronically.
New problems of ballot stuffing and the stealing of ballot boxes would be resolved with time, he added.
Obasanjo, who says he will retire to his chicken farm, promised to hand over power on time on May 29 to whoever won, even if this was his arch-rival, Abubakar.
"It's not by any means a perfect election but there is no human arrangement you can describe as perfect until when we get to God and eternity. Whatever we do is relative and I believe it is relatively good enough," he said.