Gaborone - Botswana's High Court heard a petition on Thursday challenging the constitutionality of parliamentary rules that allow lawmakers to vote for the vice president by secret ballot.
The ruling Botswana Democratic Party argued that the system - which has been used since 1998 - went against the "open and transparent" aspirations of the constitution.
The contentious rules also provide for secret ballot voting of the speaker and deputy speaker of the parliament. They were recently strengthened to include a voting booth.
The ruling party, however, wants voting to be done openly by show of hands.
"This is the Constitution of the Republic and where it has been broken willy-nilly, this is where we should repair it," BDP lawyer Parks Tafa said.
The party wants the matter to be ruled on urgently.
Government lawyer Morulaganye Chamme agreed with the BDP that the case struck at the heart of parliament's ability to function, as it could not resume business until a speaker was appointed.
"It's a very important matter that concerns the fundamentals of our society and I submit that it is urgent," he said.
Government also argued that a vice-president has to be picked soonest to avoid a constitutional crisis in the event the president died.
But lawyers from opposition parties said the secret ballot protected lawmakers from undue influence from the President.
They also noted President Ian Khama was himself endorsed as vice-president by secret ballot in 1999 and 2004.
The court action has been derided by critics as an indication Khama plans to browbeat parliament into installing his brother, Tshekedi Khama, as his deputy.
The court is due to rule on the case on Friday.
Botswana went to the polls last week in elections that saw the BDP winning with less than 50 percent of the vote for the first time since it came to power in 1966.