The decision was taken at a joint meeting of the Unity board and parliamentary faction at the Saeima.
However, Aboltina's candidacy still needs to be approved by a vote of the board and the party's MPs.
Sadurskis said such a vote would only take place after Christmas, during which time party bosses are expected to try to persuade the substantial number of Unity MPs who do not back Aboltina to change their minds.
"This will happen between Christmas and Dec.28," Sadurskis said.
"The party's statutes oblige all MPs elected to parliament from the Unity list to support this candidate," the politician said - a clear warning to potential rebels that dissent will not be tolerated.
"One candidate - Solvita Aboltina - was nominated during the joint meeting of the parliament faction and the party board," Sadurskis added.
He explained that Unity members at the joint meeting of the parliament faction and the party board did not vote, only nominated the candidate.
Saduskis also revealed that Unity members also discussed possible coalition models at Tuesday's meeting but did not elaborate on the debate citing tactical considerations.
Asked if Unity might split after the vote on Aboltina's candidacy, Sadurskis said that there is never complete unanimity on all questions in any organization.
"It is not clear how many votes Unity has at the moment. We will know the answer to this question when we have a full list of faction and board members, showing also how each of them has voted," Sadurskis said.
Latvian President Raimonds Vejonis has given parties until the end of the year to come up with their nominees for Prime Minister and their suggested coalition models.
The National Alliance has repeatedly said it would not join a coalition that would be led by Aboltina as prime minister an repeated an explicit re-statement of the fact Tuesday night.
Nacionālās apvienības pozīcija ir un vienmēr paliks skaidra: pic.twitter.com/Nm0m0jwA6f— Nacionālā apvienība (@VL_TBLNNK) December 15, 2015
"The National Alliance's position is and always remains clear: The National Alliance will not support Solvita Aboltina in the position of Prime Minister," the party tweeted.
However, despite being very clear about who they will not support, the National Alliance has not said who they will support and are yet to announce their own candidate for the job.
The centrist Greens and Farmers Union (ZZS), meanwhile, has said it would not join a coalition that does not include the National Alliance. It is thought that ZZS might nominate MP Maris Kucinskis - a former senior figure in now-defunct People's Party and then the For The Good of Latvia party as its nominee.
Ironically, Kucinskis was wooed by Unity to join its ranks a couple of years ago but opted for ZZS instead.