Murray-Bruce made this call on Friday following the Supreme Court's dismissal of Atiku and Obi's challenges contesting Tinubu's victory in the February 25 Nigerian presidential election.
Tinubu's election as Nigeria's president and the victor of the 2023 presidential contest was upheld by Supreme Court Justice John Okoro.
However, the PDP declared that it was "appalled" by the Supreme Court's ruling upholding Tinubu's victory in the presidential contest.
In a statement released on Thursday, Debo Ologunagba, the PDP spokesperson, said that Nigerians have been let down by the Supreme Court's decision and that it is sad.
In response, Murray-Bruce stated that it is only proper, appropriate, and sportsmanlike for Atiku and Peter to congratulate President Tinubu on his election win.
"Litigation needs to stop, and the Supreme Court needs to stop it. He posted on X (previously Twitter) that "all talk by some persons that 'Bola Tinubu is not my President' is frivolous and unhelpful."
"You do not have 'your' President as long as you identify as a citizen of the Federal Republic of Nigeria.
"Whether you like it or not, the President of Nigeria serves as both the Head of the State and the Commander-in-Chief of the Armed Forces."
Murray-Bruce has also challenged the PDP to work on uniting their ranks since they have an obligation to fulfill as Nigeria's most viable opposition party.
He said they lost the 2015 election because to division and betrayal of President Goodluck Jonathan; they would lose the 2023 election due to division as well. If they allow this to happen a third time, he said, they will be destroyed.
The Nigerian youth were cautioned by Murray-Bruce, a senator from Bayelsa East from 2015 to 2019, not to allow any candidate, political party, or television network to incite them against the government.
"You, the Millennial generation, own the future; we, the fifty and sixty-year-olds, do not. Apply it wisely. Plan for 2027 now, or suffer when that day comes," he said.