In separate statements, the countries said the action of Buhari could have effect on the general election.
The chief justice could preside over a disputed election result.
Nigeria's chief justice, Walter Onnoghen, could have ruled on any dispute of election results, which are widely expected in Nigeria's 2019 elections, now scheduled on February 16.
He explained that decision to suspend Justice Onnoghen was at the request of the Code of Conduct Tribunal (CCT) over allegations that he failed to declare his assets.
Onnoghen had been on the verge of swearing in judges of election tribunals.
Buhari, of the All Progressives Congress (APC), came to power in 2015 on a pledge to stamp out corruption and is seeking another four-year term.
"It risks affecting both domestic and global perceptions on the credibility of the forthcoming elections", the statement reads.
The move - after a complaint reportedly made by Buhari's former spokesman - was immediately condemned by opposition parties as a government attempt to manipulate the judiciary.
"Our country is falling apart under the leadership of President Buhari and it is time to stand up for democracy", the main opposition candidate, Atiku Abubakar, 72, said in a statement.
Saraki said the president has sent a wrong signal to the world by unilaterally taking a decision of such magnitude and not following the provision of the constitution. An appeals court on Thursday ordered the suspension of the trial.
The group also commended the present administration "for the smooth take-off of academic activities at the Nigerian Maritime University, Okerenkoko", as well as the president's directive for the "approval of the dredging of the Escravos Warri River at the cost of N13billion to enable cargo vessels access Warri sea port, which will in turn boost economic activities in the Niger Delta", among other listed achievements.
Buhari on Friday pointedly accused the apex court of frustrating government efforts to tackle corruption by overturning graft convictions.
The judge had admitted a failure to comply with assets declaration requirements, he said, adding: "The suspension is morally justified and legally justified".
"The Constitution of Nigeria is explicit in stating that the Chief Justice of Nigeria may only be removed from Office upon a motion supported by two-thirds of members of the Nigeria Senate on specified grounds".
Debo Adeniran of the Coalition Against Corrupt Leaders lobby group also backed the president and said the judiciary had frustrated the fight against corruption.