In what Mr. Harbinson sees as a move offering local people the chance to have their questions answered, the TUV is holding a public meeting in Dromore Town Hall at 8pm on Friday, February 8.
And he invited Mr. Stewart to take part and allow the people of Dromore to decide for themselves.
"We have had a lot of things said by the DUP over our ability to deliver for the people of this area," he said, "and I feel the time is now right to have these matters addressed."
Mr. Harbinson said that the TUV being a new party, fighting its first election, did not mean it was not in a position to deliver for the electorate.
"Many voters fear change and are daunted by the possibility of voting for something new and different," he said, "but I would urge everyone to come along to the public meeting and help us alleviate those fears.
"We believe that we can offer a better future to the people of Dromore and District and Northern Ireland as a whole, and would ask the electorate to come along and pitch their questions to us, so that we may provide them with the full picture, that they can then make an informed choice thereafter."
He added, "Our party leader Jim Allister MEP is on record as having invited Dr. Paisley to come along and debate with him, but it would appear that Dr. Paisley is unable. or perhaps unwilling. to do so, so I would therefore ask Mr. Stewart to come along and share the platform with me so that the electorate can assess the merits of our policies, which Mr. Stewart and his party have been so quick to dismiss for themselves."