The Democratic Alliance wants Speaker Baleka Mbete to make her decision known by Friday on whether the vote in the motion of no confidence in President Jacob Zuma will be by secret ballot or not.
"It is our belief that there is no reason why the Speaker cannot apply her mind and duly communicate her decision on the secret ballot by close of business this Friday, 21 July, instead of waiting until a day or two before the vote, as Mbete suggested in a recent interview," DA Chief Whip John Steenhuisen said on Monday.
On Sunday, Parliament said in a statement that Mbete would make her decision before the vote took place on August 8.
The Constitutional Court ruled on June 22 that Mbete had the constitutional power to prescribe that voting in a motion of no confidence in the president could be conducted by secret ballot.
In Sunday's statement, Parliament said Mbete had received submissions from nine of the 13 political parties about the appropriate voting procedure for the motion.
"Both the African National Congress and the Democratic Alliance have indicated they will abide by the Speaker's decision, while the rest of the nine prefer a secret ballot," read the statement.
Steenhuisen said it was incumbent on Mbete to decide if the voting would proceed via secret ballot.
"We emphasised this in a letter responding to her curious request for 'political parties to submit their views regarding their preferred means of voting'," Steenhuisen said.
"Mbete rarely concerns herself with the views of other political parties, or even contrarian views within the ANC. It is disingenuous for her to pretend to care now that she's been singled out for not doing her job. She cannot shift her responsibility. She, and she alone, must make the decision and it must be rational."
He reiterated opposition parties' call for Mbete to recuse herself from presiding over the debate on the motion.
"The Speaker has a long history of showing bias in her slavish defence of President Zuma," he said.
Mbete indicated over the weekend that she would not recuse herself. On previous occasions she denied accusations of bias and refused to recuse herself.