The vote was on whether to change the policy that decides how the city's police officers interact with ICE. City leaders received an amended version on Tuesday as Houston Mayor John Whitmire said he had been working with the state.
PREVIOUS REPORT: Mayor Whitmire proposes amendment to HPD immigration policy that 'reaffirms Fourth Amendment'
Earlier this month, the council passed the controversial policy, eliminating the requirement for Houston Police Department officers to wait 30 minutes for ICE to respond.
That triggered a reaction from Texas Gov. Greg Abbott, who claimed Houston was violating an agreement with the state.
The governor said the city could lose $114 million in public safety funding from the state if the ordinance was not amended.
In the proposed version presented by Whitmire on Tuesday, one amendment states that nothing in the ordinance limits "cooperation with federal immigration authorities as required by state law or agreement."
Another states officers can temporarily detain someone "as long as reasonably necessary to complete the legitimate purpose of the initial stop or investigation and for other legitimate purposes discovered during the detention."
A big part of the debate on Tuesday was what would happen with the 30-minute rule.
READ MORE: Houston council members raise concerns over last-minute changes to ICE policy
Some council members previously said that any changes could cause fear within the immigrant community. The mayor, however, said the city could face a crisis if it loses money.