South Yorkshire Police said it is working with forces in England and overseas to find Simon Reynolds, who failed to return to court yesterday to hear a jury find him guilty of four counts of theft.
Detectives said they were following a number of lines of enquiry and investigations are ongoing with international police force, Interpol.
Reynolds, 50, was convicted of keeping around £24,000 of fees given to him for weddings, funerals and graveyard memorials when he was priest-in-charge of All Saints Church in Darton, near Barnsley.
The Church of England vicar left Sheffield Crown Court at lunchtime yesterday and did not return.
Today, the Bishop of Wakefield urged him to come home.
Bishop Tony Robinson said: "Simon, we would like to assure you that you are in our prayers and all our thoughts at this difficult time.
"We are very concerned for your well-being and urge you to be in touch and allow justice to take its course. Never forget we are praying for you."
Detective Chief Inspector Steve Whittaker said: "Simon, your friends and colleagues are very worried about you and we need you to get in touch with police.
"It is in your best interests to return as soon as possible and allow the justice process to take its course."
Reynolds should have handed over the money to the diocese and the parochial church council, the court heard.
Prosecutor Tom Storey told the court that investigations by the church and police showed Reynolds had only passed on a fraction of what he should have between March 2007 and March 2013.
The offences were described as a "significant breach of trust".
A Joint statement from the Diocese of West Yorkshire and the Dales and the Diocese of Guildford expressed concern for the well-being of Reynolds.
It added: "We ask people to keep Simon and his family in their prayers and urge him to get in touch to allow justice to take its course."
The Archdeacon of Pontefract, the Ven. Peter Townley, said: "Our thoughts and prayers are with all of those affected by this crime.
"We deeply regret any further pain caused to those families who paid fees to Simon for funerals and our hope is that this conviction now affords some peace.
"The consequences of Simon's actions have been felt far and wide, not least by parishioners here in Darton but also in Farnham, Surrey, to where he moved in March 2013.
"It is of course a matter of deep disappointment when a member of clergy acts in anything other than an exemplary manner.
"Simon, as with all other members of clergy, received training and advice on how to handle all fees paid to him directly and the court has found that he knowingly flouted this advice and kept the money for himself."