The Reverend Simon Thomas, 44, of Hythe, Hampshire, admitted the charges at Southampton Crown Court.
The court heard he had used internet chatrooms to groom his victims.
Thomas, who had worked in Hythe for 10 years, has been suspended by the United Reformed Church and disciplinary proceedings will now continue.
Most of the offences took place during the last three years, the court heard.
The charges against him included inciting children to engage in sexual activity, meeting children following sexual grooming, indecency with a child, sexual activity with an 11-year-old and making indecent photographs of children.
Thomas pleaded guilty to all 35 charges against him.
Judge Jeremy Burford QC adjourned sentencing until 28 July for reports to be carried out, but indicated he was considering imposing a life sentence.
After the hearing, the father of one victim said discovering his child had been groomed and abused by Thomas had been "devastating" for his family.
The child's computer was in the family's front room but they were unaware the boy was being targeted.
He said he wanted to warn other parents to be aware of the dangers of internet chatrooms.
The Reverend Adrian Bulley, moderator of the Wessex Synod of the United Reformed Church, said the church had been left "deeply shocked" by Thomas' actions.
He added: "The church takes abuse of this nature with ultimate seriousness and is committed to the protection of children and young people - a commitment that is embodied in an exhaustive policy of child protection.
"The church has cooperated fully with the relevant authorities in their thorough investigations of his conduct as a minister."