The 43 percent is 3 percent less than in 2000, the Gallup Poll said. But the drop is statistically insignificant because it's within the poll's 4 percent margin of sampling error.
The 35 percent of respondents wanting the federal government to reduce its involvement rose 6 percentage points from 29 percent in 2000, Gallup said.
The results suggest Americans are largely "content with the current level of federal involvement in education" from kindergarten to 12th grade, Gallup said.
Parents of school-age children are particularly supportive of expanding the government's role in education, with 56 percent favoring more involvement.
Sixty percent of Republicans favor less federal involvement in education while 63 percent of Democrats want more. Independents prefer more involvement over less 44 percent to 33 percent, Gallup said.
The same poll finds 54 percent of Americans dissatisfied with the quality of U.S. K-12 education, the highest percentage Gallup has recorded since August 2000.
But parents are largely satisfied with the quality of their own children's education, with 80 percent saying they're either completely or somewhat satisfied, the highest percentage Gallup reported since first asking the question in 1999.
Gallup polled 1,013 adults living in the continental United States Aug. 5-8.