Police allege they posed as a 13-year-old girl on the internet to catch Robert Fuller, from All Saints Catholic Parish at Liverpool.
They allege he sent chat-room messages between July and August, and even tried to arrange a meeting to engage in sexual activity.
Police arrested Father Fuller in a car park at Parramatta, in western Sydney, at 12.30pm yesterday, and later charged him with grooming a person under the age of 16.
He was refused bail and will appear in Parramatta Local Court today.
During yesterday's operation, police also seized laptop computers, documents, photographs and a mobile phone from the presbytery at All Saints Catholic Parish on George Street.
Three schools, including a primary school and separate boys' and girls' colleges, are next to the presbytery.
A Catholic Education spokesman said Father Fuller was not on the teaching staff at either school.
Detective Superintendent John Kerlatec, commander of the Sex Crimes Squad, said the man allegedly had several conversations and sent several sexually explicit images during a three-week period. He allegedly used a number of different websites.
Mr Kerlatec urged parents to speak to their children about the dangers of the internet.
"The internet can be a great tool for children. However, social networking sites can be potentially dangerous for children if they are left unsupervised," he said in a statement.
"Regular online operations are conducted by detectives at the Child Exploitation and Internet Unit in an effort to detect online sexual predators.
"The role of parents however, is crucial with assisting in the prevention of child internet exploitation."
A Sydney Catholic Archdiocese spokeswoman said officials were made aware of Father Fuller’s arrest yesterday.
He was immediately stood down and would not be returning to the parish, she said.
Father Fuller had also arranged to stay outside the Sydney area while the matter was before the courts, she said.
The Sydney Archdiocese was not aware of any complaints being made about Father Fuller in the past, she said.
Father Fuller was ordained in 1979 after studying at St Columba's College at Springwood, then St Patrick's College at Manly.
He was appointed parish priest for Liverpool in 2003 and has a Bachelor of Theology from the Catholic Institute of Sydney.
