HOUSTON (FOX 26) - "While we acknowledge that we are making progress, we also want to be very clear the recovery is not happening fast enough for any of us," Turner said.
As of Feb. 20, more than 3,420 households from Houston remain in hotels and thousands more are living in homes in dire need of repair, he said.
Houston is also working to repair the $2.5 billion in damage that city buildings and other infrastructure suffered, including its municipal courts building and performing arts center.
Delays in federal funding have also resulted in the postponement of a program that will pay up to $60,000 to repair damaged homes. Repairs on the first 10 homes under this program are scheduled to begin next week.
But Turner touted the city's quicker than expected pace in cleaning up debris from Harvey. As of Friday, more than 1.7 million cubic yards of debris - enough to fill more than 13,400 buses - had so far been collected.
Rebuilding efforts are going forward as the city has received nearly 8,900 Harvey-related repair permit applications.
Turner also touted the efforts of volunteers and nonprofit groups who have helped in the recovery efforts, including with the cleaning out and repairing of homes.
"With the federal dollars coming slowly and people in need right now, but for the nonprofits and the volunteers, immediate needs would not be met," Turner said.
For the Texas Organizing Project, a nonprofit that's worked on finding housing for low income residents and other issues since the storm hit, its focus is still "very heavily in Harvey," said spokeswoman Mary Moreno.
"For us it's still there. We're still meeting with officials almost every day," Moreno said.
A new volunteer program called "Houston Still Needs You" is set to launch on Saturday. City officials are negotiating with the Federal Emergency Management Agency about counting the hours that volunteers provide for relief and recovery services as payment for the local match Houston must pay to get the disaster grants.
Turner said it likely won't be until after summer when Houston gets its share of a $5 billion grant from the U.S. Department of Housing and Urban Development that can be used to repair damaged homes, businesses and infrastructure. It's unclear when or how much Houston and the rest of Texas will receive from $90 billion in federal disaster relief aid that Congress approved earlier this month to help those impacted not only by Harvey but by hurricanes Irma and Maria and the California wildfires.
An analysis by The Associated Press has shown that efforts in Texas to provide short-term housing for victims and emergency repairs to get people back in their damaged houses have lagged well behind earlier post-disaster efforts.
FEMA officials have acknowledged such efforts have not moved as fast as they would like but that hundreds of thousands of homeowners are already repairing or rebuilding their damaged houses and their recoveries are being supported by billions of dollars in federal grants, Small Business Administration disaster loans and flood insurance payments.