Earlier this week officials said it could take crews between three and five weeks to shore up the mile-long stretch of the interstate after a suspected arson last Saturday burned about 100 support columns.
"The bridge structure itself seems to be in better shape than we anticipated," Newsom said during an evening news conference. "One thing we can guarantee you is we will be open, five lanes in both directions, at the latest Tuesday of next week."
More than 250 people were working around the clock to make the repairs, he said.
"This is a good day in Los Angeles," Los Angeles Mayor Karen Bass said.
Earlier Thursday, Bass, who also chairs the Metro Board of Directors, introduced a proposal with a series of steps she wants the transit agency to take to encourage the use of public transportation during the extended closure of the freeway.
Among the directives included in the motion are a lifting of the ride cap for Metro low-income fare LIFE program, coordination with local jurisdictions to speed up trains and buses in the closure area and increase the number of "Transit Ambassadors" on the system to assist riders, particularly those who may be riding for the first time.
The motion also calls for free use of the Metro Bike-Share system during the closure and reduced daily parking rates of 10 cents at Metro Park and Ride lots.
"Metro has reported that ridership on the E (Expo) Line is up 10% which runs parallel to the freeway," Bass said in a statement. "This shows that our message to take Metro during the closure is resonating, but we have an opportunity to do more to address the impacts for communities and commuters during the closure and beyond, and that is what we will continue to urgently work toward."
Bass, Metro board members seek to boost public transit during 10 Freeway closure in downtown LA
Several other Metro board members seconded the motion, including county Supervisors Janice Hahn, Holly Mitchell and Hilda Solis, Whittier Mayor pro tem Fernando Dutra and Glendale City Councilman Ara Najarian.
"This is about common sense solutions to help more people get where they need to on the bus or train while we fix the I-10 as quickly as possible," Hahn said in a statement.
Bass earlier directed the Los Angeles City Department of Transportation to make Commuter Express and DASH buses free to encourage commuters to use public transportation. She also requested an increase in the number of white-glove traffic officers in congested areas to assist commuters through busy intersections.
The fire that spread quickly over 8 acres was fed by pallets, cars, construction materials, hand sanitizer and other items being stored under the freeway in an industrial neighborhood. No injuries were reported, but at least 16 homeless people living in an encampment there were taken to shelters.
The arson investigation was ongoing, officials said. No arrests have been made and Newsom has said investigators are trying to determine if more than one person was involved.
An estimated 300,000 vehicles use the stretch of freeway daily, which runs east-west across the heart of the metropolis and connects with other major highways. The city has been urging people to avoid the area, take buses and trains, or work from home.
The Associated Press and City News Service contributed to this report.