Douglas Carswell, who held his Clacton seat, praised Mr Farage as a “heroic and inspirational figure” but told the Times: “I am not going to be running as leader.”
He said: “There will be a leadership election for the next leader of Ukip in September and I will consider over the course of this summer whether to put my name forward to do that job again.”
Mr Farage said he would recommend Ukip Deputy Chairman Suzanne Evans to be stand-in leader until the leadership challenge is complete.
He lost to Conservative Craig Mackinlay in Thanet South by almost 3,000 votes, leaving Ukip with just one MP after former Tory Mark Reckless lost in Rochester and Strood.
Announcing his resignation yesterday, Mr Farage said: I’m a man of my word. I shall be writing to the Ukip national executive in a few minutes, saying I am standing down as leader of Ukip.”
Earlier in the day, Mr Farage railed against an electoral system which handed the SNP 56 seats and Ukip one, even though his party was the third largest by vote share.