On Monday, Balderrama said he planned to 'own' his mistakes in an email sent to his department.
"My actions did not meet the standards of who I am as a man of faith, husband, or father," Balderrama wrote.
"I own my mistakes, they are mine and mine alone to bear, and I will pay for those mistakes for the rest of my life."
Balderrama went on to ask for forgiveness from the department's staff members, writing that he understands if they are 'upset and disappointed.'
The Chief's message comes after city officials revealed last Thursday that Balderrama was under investigation for his alleged involvement in an inappropriate relationship while off-duty.
Officials say Balderrama informed the city of the accusation in February.
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The city has previously said Balderrama will remain on duty in his position as chief at least until the investigation is finalized.
On Friday, leaders of the Fresno Police Officers' Association questioned the ongoing investigation in a message sent out to union members.
"This is an incredible offense to every sworn member of the agency, who is held to account for policy violations surrounding "discretion" and "conduct unbecoming," Board President Brandon Wiemiller wrote.
Union leaders have called for an emergency board meeting on Wednesday to further discuss the investigation.
Stay with Action News for the latest updates on this developing story.