Warner told the council weeks ago that he planned to step down after 23 years of service, as of Nov. 1.
However, council members reportedly asked the attorney to stay on until a replacement could be found.
Warner had assured the council that he would not leave them without a city attorney.
Council members also voted to accept a termination agreement with Alpha Reclaim, a company that had contracted with the city for the use of wastewater treatment plant effluent.
The company had planned to sell the effluent for use in fracturing shale formations for oil and gas producers.
Company Vice President Reagan Scott told the council that natural gas development had not progressed at the level his company had expected.
He said he would like to maintain communication with the city in anticipation of a future opportunity to enter into another agreement.
Councilman George P. “Trace” Morrill made the motion to accept the agreement, and Mayor David Carabajal seconded the motion.
The two council members voted in favor of the motion, and Mayor Pro Tem Libby Spires abstained from the vote. Councilmen John Fulghum and Santiago “Jimbo” Martinez were not at the meeting.
Council members also voted unanimously, following the executive session, to enter into an agreement with Texas First Group for a possible contract to employee an interim city manager.
City Secretary Barbara Treviño has been filling in for that position since the termination of former City Manager Deborah Ballí.
Ballí has since accepted a position as finance director for the City of Kingsville.
The council could possibly take action on hiring an interim city manager as early as next week.