Mayor Sylvester Turner said Saturday that water pressure would be improving for homes, though it wasn't yet clear when the boil order would be lifted.
Water samples were expected to be sent to a lab Saturday to determine whether it was safe for consumption, Turner said. Results were expected late Sunday.
During remarks at a city water distribution site, Turner asked that car washes in the city remain closed for the weekend.
"I know it's a beautiful day and normally in the city of Houston, people would rush to get their cars washed," Turner said. "I'm going to ask that you hold on that car washing, and I'm going to ask even car washing companies, businesses, if they will hold for this weekend. Let us get past this crisis. Then you can proceed, I promise you. In the city of Houston, warmer days are coming."
Water outages across Houston and Texas have been widespread, and damage to some supplies was catastrophic due to the sub-freezing temperatures this week.
Water supply issues were a bigger challenge due to at least two separate problems: Widespread power outages and broken equipment.
Harris County meteorologist Jeff Lindner shared photos Thursday of several components at some water supply systems.
"Damage is extensive," Lindner said.
In addition to water supply restoration, the city is making efforts to establish a relief fund, according to Turner. An announcement on it was expected to come Monday.
Approximately 590 public water systems in 141 Texas counties reported disruptions in service, affecting nearly 12 million people as of late Wednesday afternoon, according to a Texas Commission on Environmental Quality spokesperson.
"It's not clear when water supplies will be replenished, but energy constraints often have impact on the water system because the water system requires energy for treatment and pumping," said Michael Webber, an energy resources professor at the University of Texas at Austin.
13 INVESTIGATES: 48 hours without power a 'nightmare' as residents demand answers
Until the city gets its water back up and fully restored, Haddock urges people to limit their water use.
While utilities worked to restore service, homes and businesses may not be able to receive service until damage is repaired after burst pipes were reported. Power outages only made those situations worse, officials said.
"If you don't have any power, you're not even warming your homes at all, so the houses are just standing there with no power, pipes are going to freeze .... just like mine did," he said. "My pipes froze, and when the power came back [Tuesday] afternoon, my pipes burst. It's happening to everyone. This is a storm with no respect for persons."
In Galveston, water supply levels were holding steady Thursday morning, but they weren't increasing, city officials said.
"We will keep the water service on as long as possible, though intermittent disruptions may be necessary as we attempt to stabilize the water supply due to major water line breaks across the island," said public information officer Marissa Barnett.
Pump stations on 30th Street and the airport were running, but officials said they were aware of many areas of the city that were still experiencing issues.
Boil orders across the state could last longer than usual due to the unprecedented number of water supplies that were compromised by outages and pressure issues, according to Texas Commission on Environmental Quality Executive Director Toby Baker. Baker says testing will have to be conducted to ensure water is safe before the orders can be lifted.
There are only 135 labs in the state that do that sampling, he said.
The Texas Tribune contributed to this report.