"The IFP has formally approached us to establish coalition governments, but we have made it clear that the process of negotiations will not start if they don't apologise," NFP leader Zanele Magwaza-Msibi said on Wednesday.
There has been a war of words between the parties since the NFP was formed earlier this year.
The IFP has accused the NFP of being an African National Congress project aimed at destabilising the IFP.
"The allegations that we are an ANC project mean that they don't take us as a party. That is why they have to withdraw before we start the negotiations," said Magwaza-Msibi.
Coalition talks with ANC
The NFP has already held coalition talks with the ANC. On Tuesday, the party received a report from a delegation that met the ANC on Monday.
"We received the report and the process is still continuing," said Magwaza-Msibi.
The Witness newspaper reported that IFP leader Mangosuthu Buthelezi was initially against the idea of approaching the NFP, but that party leaders convinced him to change his mind.
However, this was denied by IFP national treasurer Narend Singh.
He confirmed that the IFP had approached the NFP, but said his party was not aware of the NFP's conditions.
"We have formally approached them and we are waiting for the response," he said.
Singh said Magwaza-Msibi phoned him on Tuesday morning and told him that the party would send the IFP a letter.
"I don’t know whether the issue of the condition is contained in that letter, which we have not received," he said.
19 hung municipalities
The May 18 local government elections resulted in 19 hung municipalities in the KwaZulu-Natal.
The political parties need to conclude coalitions so councils can be formed in these municipalities.
The NFP, which won Edumbe municipality outright and gained a majority vote in Nongoma, is kingmaker in a number of the hung municipalities.
The ANC has a majority in 14 of them, the IFP in four and the NFP in the Nongoma municipality.
If the ANC and NFP form a pact, the IFP will be left with only Ulundi and Umsinga municipalities.
Magwaza-Msibi said no deal had been struck with the ANC yet.