This is despite objections from opposition parties, who are threatening to boycott the meetings planned for April 10 until 12.
This could thwart the long-awaited passing of the bill, first mooted by former president Jacob Zuma in 2014.
This happened on Wednesday when the committee received a briefing from the Department of Labour on the oral submissions made by labour, employee representatives and interest groups over the past two weeks.
It also took place two days after Labour Minister Mildred Oliphant said it would not be possible to implement the National Minimum Wage Bill by May 1 as had been envisaged.
Parliament is processing the bill, along with the Labour Relations Amendment Bill and the Basic Conditions of Employment Bill.
During Wednesday's committee meeting, both the EFF and DA called for enough time to consider the submissions and a response of the Labour Department when they returned from the constituency week on April 17.
The ANC agreed that more time was needed to discuss the bills and proposed the committee meet on April 10 until 12, but allowed the department to respond to the oral submissions.
ANC’s Lerato Teko called on the committee to sacrifice and give their time to deal with things decisively.
“We are not doing this for ourselves.
"We do it for the people out there,” Teko said.
EFF’s George Moteka warned that there was a rush similar to engagements in the National Economic Development and Labour Council (Nedlac).
Moteka was concerned that the department was invited on Wednesday to respond to the oral submissions from labour and employee representatives.
“The whole thing is premature The rush is still there. It is premature for the department to give a response before ourselves as the committee dealt with them,” he said.
The DA’s Michael Bagraim said he could not understand why they had to come back from their constituency time to Parliament when scheduled to return the following week.
“I don’t know what is the rush. It is almost indecent ”
He warned the ANC of possibly talking to itself if it went ahead with the meeting.
Bagraim said a redraft bill still needed to be brought to the committee.
The ANC’s Lemias Mashile said the committee wouldn't have all the time after the recess, because it would be preoccupied by other committee work.
“It is important that we create space if we are seriously honest,” Mashile said.
Moteka said the EFF would not accept any interference to the constituency week.
“Any suggestion that we leave constituency work and come back is rejected,” he said.
His sentiment was echoed by the DA’s Derrick America.
"We are available from April 17.”
Although acting committee chairperson Sharome van Schalkwyk did not initially raise the matter, the ANC nevertheless won the vote after she consulted the “principals in Parliament”.