The spokesperson for the group and Member of Parliament for Asante Akim North, Andy Appiah-Kubi, told journalists in Parliament, Accra, yesterday.
"We made a request to him and he said we should wait till the presentation of the budget and there after accede to our request so we are waiting and expect him to act," he added.
Majority of the caucus members have been pushing for the removal of Mr Ofori-Atta from office for what they said were his incompetence and conflict of interest.
They threatened to boycott the budget presentation but backed down on their demand after meeting the leadership of the governing New Patriotic Party (NPP).
A jointly signed statement after that meeting by the Majority Chief Whip, Frank Annoh-Dompreh and General Secretary of the party, Justin Kodua Frimpong, said that it was agreed that "the President would act upon the request" after the minister had presented the budget, the Appropriation Bill passed and negotiations with the International Monetary Fund were concluded.
The 'rebel' MPs, however, have developed a cold feet towards the debate of the budget and have stayed away from same in what political watchers said was a silent protest against the continuous stay in office of Mr Ofori-Atta.
Mr Appiah-Kubi, who was not present in the chamber when the debate begun on Tuesday said he could not explain why his colleagues have not showed up for the debate, but that their demands have not be shelved.
"I cannot explain why people have not come to participate in the debate, but what I can tell you is that we agreed on something and the President must act in due time.
We have not disappointed our constituents, we are just respecting the roadmap as agreed with the President and once we have accepted to respect his request for the minister to see through the budget, which we have done, we expect the President to honour his side of the agreement."
On the absence of the finance minister on the floor during the debate, Mr Appiah-Kubi said they were not even expecting Mr Ofori-Atta in the House.
The debate on the budget statement and economic policy of government for the year ending December 31, 2023 commenced with the majority caucus of the House registering a very low turnout.
At the commencement of the debate, ahead of the approval or otherwise of the budget, at about 12:20 noon on Tuesday not more than 30 of the 138 members of the caucus were present in the Chamber.
Ordinarily, budget debates, especially the days of commencement, are characterised by high turnouts but on this occasion, only the minority caucus registered more than half of their numbers in the House.