Alex Kear, who sits on Wakefield Council as an independent, admitted the charges when he appeared at Leeds Crown Court today (July 9).
The 50-year-old admitted one charge of arranging or facilitating the commission of a child sexual offence involving a child under the age of 13.
Kear also admitted one charge of inciting the sexual exploitation of a child under the age of 13.
The court heard Kear has no previous convictions and sentencing was adjourned to August 20 to allow time for pre sentence reports to be prepared.
Kear was granted bail until his sentencing hearing
Judge Andrew Stubbs QC told Kear: "The fact that I am adjourning your case for reports is no indication of the sentence that you will ultimately receive. All options remain open."
Kear, of Stansfield Drive, Castleford, won his Airedale and Ferry Fryston seat from Labour at the local elections in May last year.
His name will be placed on the sex offender's register for a period of time to be determined at the sentencing hearing.
Gillian Marshall, Wakefield Council’s chief legal officer, said after the court hearing: "Under local authority legislation, Alex Kear remains a councillor.
"Wakefield Council is powerless to remove him at this stage.
“Central government has essentially left local councils powerless to take action in these situations.
"We do not have any authority to remove elected members from their position, regardless of the severity of their alleged crimes, unless they receive a significant custodial sentence.
"Therefore unless Coun Kear chooses to resign, he remains a councillor. This will be reviewed when he is sentenced.
“As soon as we were made aware of the investigation by West Yorkshire Police we took all the appropriate safeguarding measures within our control and we will continue to do so.”