The Raila Odinga-led Orange Democratic Movement (ODM) clashed with Deputy President William Ruto over calls to amend the constitution in order to expand the executive.
ODM Secretary General Edwin Sifuna said the push for changes is unstoppable while Mr Ruto said the campaign is premature and unnecessary.
Speaking in Nakuru, the Deputy President said it is unfair to put Kenyans in a campaign mood just a few months after they had gone through a lengthy electioneering period.
He said the Jubilee administration is keen on focusing on its election pledges and would not entertain "politics of power games" being introduced by some individuals.
"Having given us an opportunity to serve you, I want you to know that our objective is to complete the development projects that we promised you and will have no time to engage in politics of power sharing," he said at a funds drive in aid of PCEA Tabuga church in Bahati, Nakuru.
"You did your part in electing us and what is remaining is for us to work for you.
"Talking of amending [the] constitution right now in order to create other political positions is to lack respect for the electorate," he told the congregation.
In Nairobi, Mr Sifuna described those against the call for the changes as selfish individuals without the interest of Kenyans at heart.
"If Kenyans decide that the solution to their problem is through a change of the Constitution, nobody will deter us," Mr Sifuna said.
"Nothing will deter our quest to discuss our issues as Kenyans."
He said the handshake between President Uhuru Kenyatta and Mr Odinga had given the much-needed dialogue on electoral injustices a chance that the party is ready to exploit.
"As ODM, we want to assure you that every solution to our problem will be discussed on the table," he said during a church service in Makadara.
The Deputy President has been critical of calls to amend the Constitution despite leading the camp that campaigned against it in 2010 on the basis that it contained laws that needed to be changed.
The tension that followed the annulment of the August 8 presidential election, Mr Odinga's withdrawal from the October 26 repeat poll on and his mock inauguration as "the people's president" on January 30 before he struck an agreement with President Kenyatta have all combined to trigger conversations about changing the Constitution.
Mr Odinga was among those who campaigned for the Constitution in 2010 and who continuously promised that the 20 per cent that needed changing would be worked on in the future.
On the political front, Mr Ruto has been working to consolidate his support as he seeks to succeed Uhuru Kenyatta as President in 2022 and a referendum comes with the risk of building an opponent's profile.
Earlier yesterday, he was reassured of support from the Mt Kenya region by Kirinyaga Governor Anne Waiguru.
"Contrary to misleading media reports, Mount Kenya has vowed to back the DP in his bid to be next president.
"Some people may have other plans but we will stand with you in this journey. Let no one sway you otherwise," Ms Waiguru said.
Ms Waiguru was among governors who attended the Eldoret City Marathon, which was flagged off by Mr Ruto.
Meanwhile, Mr Odinga has vowed to ensure all independent institutions are repaired before 2022 General Election to avoid a repeat of electoral injustices that has rocked the country for years.
He indicated that by reforming institutions such as the Independent Electoral and Boundaries Commission, it would be a step in ensuring that the country no longer holds a divisive election.
Mr Odinga asked his critics to unite with him in healing Kenya and stop asking many questions on why he did not consult his opposition colleagues ahead of famous deal with President Uhuru Kenyatta to 'build bridges'.
"We have too many commissions yet they are not as effective as they should be.
"We cannot be talking about 2022 yet we are still sorting out issues that led to the mismanagement of the 2017 elections," Mr Odinga said during Sunday service at St Peter's ACK.
Reports by Wycliffe Kipsang, Joseph Openda, Silas Apollo and Rushdie Oudia