Wiper leader Kalonzo Musyoka has asked President Uhuru Kenyatta and ODM leader Raila Odinga to "devolve the handshake".
He said doing so will erase suspicion arising from the belief that the March 9 Uhuru-Raila truce was about 2022 presidential election.
He also defended his decision to back the new tax measures in the Finance Act, 2018.
Kalonzo told Citizen TV in an interview aired on Tuesday night that the Opposition was not compromised by the handshake to support the tax measures.
He asked Uhuru and Raila to let Kenyans in on the deeper meaning of the ‘handshake’ and work to remove the cloud of suspicion around the initiative.
The handshake has been linked to the 2022 politics amid claims of a scheme to lock out critical players from the contest.
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"The ‘winner takes all’ approach has brought us problems. Any opportunity for dialogue is important. I support such initiatives, including the Building Bridges initiative," the Wiper leader, in reaffirming his support for the handshake, said.
"We must ‘devolve the handshake."
He maintained that assertions among Kenyans that only those who took part in the swearing-in be part of the handshake must be discouraged.
"To say that only those who attended the swearing-in have a right to talk about being included in the handshake is a negative approach to it. I support the principle behind the handshake," Kalonzo said.
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Speaking extensively for the first time on the tax that introduced an eight per cent charge on fuel products, the former Vice President said Wiper took its stance having understood President Uhuru Kenyatta's dilemma on the same.
"Personally, I supported the motion because I understood where the President was coming from."
"We were not forcing our members to take a position. We were just giving direction," he said, adding that the decision was taken on an understanding that the country is at a difficult position.
He said the debt situation, for which the tax measures are set to mitigate, would have been renegotiated had NASA formed government after the 2017 poll.
"It could have been possible to avoid the tax burden if the government had time to recover all money stolen through corruption. Going forward, we may have to relook at how to relieve Kenyans from the tax burden," Kalonzo said.
The Wiper boss added that there is "no way he could be proud of causing pain to Kenyans who are feeling the effects of heavy taxation.
He maintained that it is not too late for the President to take the lead and renegotiate the over Sh5 trillion debt.
"I know the agony President Uhuru Kenyatta has been going through as Head of State in explaining the VAT," Kalonzo said.
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The former Vice President also revisited the January 30 oath that he, Ford Kenya's Moses Wetang'ula, and Amani's Musalia Mudavadi skipped.
On this, he urged Kenyans to stop being held captive by the past but to assess the current situation and focus on the future.
Kalonzo said Raila knew he was not going to take the oath adding that he is elated that Kenyans eventually referred to the Uhuru Park event as a 'mock swearing in'.
"Between Raila and myself, he knew I was not going to take that oath. My friend Raila Odinga knew I was not going to take that oath."
However, at the height of the altercations on the oath, Kalonzo said he could not attend as "he was under house arrest."
Wetang'ula's explanation, on the other hand, was that "Raila asked them to switch off their phones".
But Kalonzo changed tune saying the NASA coalition leaders were going to be regarded as pariahs by the international community had they maintained the hard stance on the disputed August and October 2017 presidential elections.
"It is terrible when I reflect about it. I have always stood for honest politics. I'm guided by what is reasonable and that which is in the best interest of the nation," Kalonzo said, further calling on leaders to ensure they don't act in a manner that misleads the people.
The NASA principal reiterated that there were people who misadvised Raila about the January 30 oath and that the disinformation about the event is regrettable.
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On perceived divisions in NASA, the coalition leader said they have not met to dissolve the alliance that he and Raila used to challenge Uhuru's Jubilee Party.
He said NASA can only collapse if any of three parties walked out of the coalition.
"As we speak, NASA is on paper the coalition that is in Opposition. We have not met as a summit to assess the situation and come up with a position."
Kalonzo admitted the feeling among NASA supporters that the coalition has let them down adding that it is a fact the opposition was weakened by the handshake.
The cries escalated after MPs attempt to block the new tax measures, whose passage was largely blamed on NASA, flopped.
Kalonzo further called for the reconstitution of IEBC describing the entity as 'disgraceful' and one that 'needs urgent reforms'.
He also backed calls for constitutional reforms, national dialogue, and further discouraged politicians from engaging in confrontational politics.
"We need to take a break and reflect on issues like the possibility of amending the Constitution, as we said, to change the structure of government so it is all-inclusive."
Kalonzo further hailed the DCI and DPP for the renewed war on corruption saying the same is timely.
However, he condemned the arraignment of Deputy Chief Justice Philomena Mwilu in a magistrate's court.
"If we want to arraign a DCJ, we cannot take them to a Magistrate’s court. What image are we given to that profession? At that level, that matter should have been taken before JSC," he said.
The Wiper leader also touched on 2022 politics saying he will not accept being a 'professional running mate'. He said much as there will be alignments ahead of the vote, of importance now is to discuss issues bedevilling Kenyans.