He makes no mention of the fate of undocumented students currently in legal limbo in the United States, including about 75,000 enrolled in California's public colleges and universities.
Fears of rapid expansion of school choice programs have proven unfounded.
Trump's budget proposal must still win Congressional approval. Among the deep spending cuts are $143 billion in cuts to higher education over the next decade, according to a budget summary released on Monday.
The longtime education leader says public schools must serve the needs of parents and students as the Trump administration focuses on school choice.
The president has accomplished few of the initiatives outlined in his Contract with the American Voter.
Her remarks appeared to be her strongest endorsement of public schools since taking office just over a month ago.
The Trump administration has had to overcome a series of controversies and embarrassments regarding civil rights since the November election.
Secretary of Education Betsy DeVos backtracks again on comments about historically black universities that stirred controversy.