"There's lots of research and common sense that a lot of teens struggle to get up at 6 in the morning to get on the bus or 5:30 in the morning to get on the bus," Duncan told National Public Radio's "The Diane Rehm Show."
He said he understood school-bus logistics -- not only to school but also to after-school sports -- were a key force in starting high school days around dawn and ending them in mid-afternoon.
"But at the end of the day, I think it's incumbent upon education leaders to not run school systems that work good for buses but that don't work for students," said Duncan, who ran the Chicago Public Schools, the nation's third-largest school district with more than 400,000 students, before joining the Obama administration.
Duncan started a debate on high school start times on Twitter Aug. 19 when he wrote, "Common sense to improve student achievement that too few have implemented: let teens sleep more, start school later."
He told the program he meant "to challenge the status quo and be provocative" with his Twitter message.
"Study after study has shown mornings are very difficult [for teenagers]," Duncan told the program. "They're not very awake -- they're groggy, they're not able to pay attention in class," he said.
Starting later would increase teens' chances of being focused and concentrating so they can get more out of their school day, he said.
"So often in education, we design school systems that work for adults and not for kids," he said, citing current high school hours as "another example of that."
Duncan said Washington would not mandate a later start time. That decision would be left to the nation's 15,000 school districts, he said.
But he encouraged districts to challenge the existing state of affairs and consider a later start time.
"The vast majority of districts are just sort of conforming to the status quo, rather than being creative and innovative," he said.
"I would love to see more districts contemplating a later start time," he said.
At least 27 school districts have started schools later and have shown substantial successes, including increased student attendance, decreased student lateness and better grades, the Start School Later advocacy group said.
"The portion of students reporting at least 8 hours of sleep on school nights jumped from about 16 percent to almost 55 percent," St. George's School in Middletown, R.I., reported.
"Reports of daytime sleepiness dropped substantially, from 49 percent to 20 percent; first-period tardiness dropped by almost half, and students reported having more time to eat a hot, more nutritious breakfast," the school said.
Teen driver crash rates fell 16.5 percent in two years, Fayette County Public Schools in Lexington, Ky., reported, adding the rest of the state saw an increase in teen crash rates.
Many districts also reported saving sizable amounts of money, said Start School Later, which seeks to make school hours "compatible with health, safety, equity and learning."