Ian Paisley Jnr has said he is delighted by the support he has received since announcing his resignation.
Ian Paisley Jnr will continue as an MLA for North Antrim
He was speaking at one of his last functions as junior minister.
At the event, to promote the North West 200 motorcycle race, he said the public had been very positive.
"If I was a dosser, a time-waster, if I was someone who just used the position for position's sake, I couldn't show my face to people," he said.
"I have been overwhelmed by the amount of calls, letters and the reaction I get when I go into public."
Earlier on Wednesday, Northern Ireland's First Minister Ian Paisley refused to answer questions about his political future during a trip to Scotland.
He and Deputy First Minister Martin McGuinness held talks with the Scottish First Minister, Alex Salmond.
Afterwards, Mr Paisley said he would not be discussing the internal affairs of the DUP with the media.
The delegation included Mr Paisley Jnr, who remains in place as a junior minister until a replacement is found.
When asked about his future, Mr Paisley told one journalist: "I have a fairly hard rhinoceros skin - and I think I will not be skinned by you or the likes of you."
The Irish delegation visited the Scottish Parliament where they met Presiding Officer Alex Fergusson, before touring the building.
They then took part in talks with Mr Salmond at Edinburgh Castle.
A declaration making a commitment to consider urgently the feasibility study on the possible reinstatement of the Campbeltown-Ballycastle ferry service as soon as it is available, was later signed by Mr Salmond, Mr Paisley and Mr McGuinness.
"We are pleased that following close work between the two administrations significant progress has been made towards appointing a consultant to undertake a new economic appraisal," Mr Salmond said.
Mr Salmond said the two administrations had also discussed the possibility of electricity inter-connectors to handle the "vast" potential of marine renewable energy.
The Stena Link port development in Belfast and road infrastructure around the Loch Ryan corridor were among the issues under discussion, according to Mr Paisley, as well as the road fuel duty escalator and the need for "urgent representations" to the British Government about the issue.
He said: "There's growing up an intricate and very intimate proposition that the three parts of this United Kingdom that have devolved governments can do well for each part, but we can do better if we do it together and we are determined to do that."
Mr McGuinness said the visit had been useful in building on the "growing links" between Edinburgh and Belfast.
Mr Paisley and Mr McGuinness later joined Mr Salmond in South Queensferry to look at designs for the new Forth Road Bridge.
They are due to visit an anti-sectarianism project at Murrayfield.