The opposition party, which was in power from the start of civilian rule in 1999 until Buhari's 2015 election victory with his All Progressives Congress (APC) party, said the judge's suspension was a "brazen assault on the constitution".
President Buhari announced Friday that he would suspend Onnoghen, pending the resolution of a corruption trial at the Code of Conduct Tribunal.
Buhari's main challenger in February 16 vote, Atiku Abubakar, a 72-year-old businessman and former vice president who's running for the People's Democratic Party, condemned the decision.
He was cleared of similar non-declaration of assets charges on appeal at Onnoghen's Supreme Court past year.
Ologbondiyan who is also the Director, Media and Publicity, PDP Presidential Campaign Organization (PPCO) said that the PDP firmly held that such impunity could not stand, as Nigeria is a nation governed by law.
He said, "The government should as a matter of urgency, lift the suspension on the Chief Justice since the Chief Justice as so much to on his own admitted that he did not declare his assets, he should do the needful by calling it quits".
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We note widespread Nigerian criticism that this decision is unconstitutional and that it undermines the independence of the judicial branch.
Under the Nigerian constitution, the Senate has to approve an application for the removal of the chief justice by a two-thirds majority.
Opposition parties previously criticized Onnoghen's case and called it an attempt by the government to intimidate the judiciary before the election. This is the first time a chief justice is standing trial in Nigeria, where corruption is widespread. "They know that Nigerians have rejected them because they have failed in the past", he said.
"There are already the general belief that this action was taken to pre-empt the already scheduled inauguration of election petition tribunals by Onnoghen".
"They all have different roles to play in that process, " he said.
Buhari has been accused of surrounding himself with people from his home region.