James Percival, 66, said he gave mouth-to-mouth resuscitation to newborn Jonathan Percival in the vicarage in Freckleton, Lancashire, in 2014.
But Ruth Percival, 30, said she had not seen him make any attempts to revive the baby.
The inquest was halted in October when new medical evidence led the coroner to refer the case to prosecutors.
In March, the Crown Prosecution Service said there remained "insufficient evidence" to charge anyone.
The hearing at Blackpool Town Hall was told that Miss Percival, who has some special educational needs, visited her GP surgery in August 2014 to arrange to terminate a pregnancy, but had been unable to have one because she was too far gone.
She agreed she had put her "head in the sand" about the pregnancy and had not told her parents because she was "scared" of their reaction.
Mr Percival, who at the time was the vicar of Holy Trinity CE Church in Freckleton, said after she returned home from work in the afternoon on 25 November she spent time in the downstairs toilet.
He said at about 15:30 GMT he saw her come out of the bathroom carrying a towel covered with what he believed to be excrement and went outside with her to put it in a bin "when Jonathan's leg came in sight".
He told the court: "I said to Ruth, 'this is a baby, you can't put a baby in the bin'."
He said he placed the baby on the towel on the floor outside and attempted to resuscitate him.
He said the baby "was very, very cold, absolutely lifeless", adding: "The baby was quite clearly dead."
The inquest heard that medical evidence showed the baby was alive at the time he was born.
Miss Percival said she thought she saw the baby trying to take a breath, but also said: "I kind of thought I did have a miscarriage because to me the baby was dead when he came out of me."
Miss Percival and her father gave evidence that Jonathan had the umbilical cord wrapped round his neck.
The hearing is due to continue on Tuesday.
A former vicar tried to revive his daughter's baby son after she gave birth in a bathroom, an inquest heard.