Ulster Unionist Cecil Walker said he told David Trimble he would leave the North Belfast race if he wanted him to.
The offer came after 76-yr-old Mr Walker stumbled his way through an interview for Ulster Television's Insight programme during which he appeared not to understand many of the questions put to him.
Mr Walker said he experienced severe hearing problems and difficulties with his hearing aid during the broadcast.
His appearance drew much criticism from members of the public and callers to a BBC phone-in the following day.
However Mr Walker said he has been overwhelmed by calls of support from wellswishers since the broadcast.
He has admitted he was "mortified" by his performance on the night and said he could understand if some people thought he had "lost the plot".
He said Mr Trimble persuaded him to continue in the North Belfast contest despite the adverse publicity for the party.
Mr Walker was quoted on Friday in the North Belfast News today as saying a united Ireland in 30 years time would be "no bad thing" but he told the BBC it was a 'throwaway line that has been taken out of context".
" It is time for Mr Trimble to either back Mr Walker or to sack him "
The Ulster Unionist Party is strongly in favour of Northern Ireland remaining as part of the United Kingdom and such a remark would be a great embarrassment for the party.
Nigel Dodds who is running as the DUP's candidate in North Belfast said on Friday Mr Trimble should "come clean" about his attitude to Mr Walker.
He added that the remarks quoted in the newspaper "indicate he is completely out of touch with the unionist community on almost every subject.
"It is time for Mr Trimble to either back Mr Walker or to sack him'' There has been speculation that Mr Walker, who has served as MP for North Belfast since 1983, had not wanted to stand again for parliament but was persuaded to by members of his party.
The seat is expected to be one of the closest fought constituencies with all four of the main parties believing they are in with a chance.
The other candidates standing in North Belfast are Gerry Kelly for Sinn Fein, Alban Maginness for the SDLP and Marcella Delaney for the Workers Party.