Gov. Robert F. McDonnell said Virginia will take President Obama up on his offer to excuse states from parts of No Child Left Behind, the federal education law passed under President George W. Bush.

“They had a noble goal, and that is, having a rising tide lift all boats,” the Republican governor said Tuesday on WTOP radio’s “Ask the Governor” program.

“But the problem is, I think it got eaten up with some unrealistic expectations and didn’t treat some states that already had high achievements well, in terms of monitoring adequate yearly progress,” McDonnell said. “An unusual amount of federal bureaucracy soaked up some of the money.”

Last week, the Obama administration offered details of its plan to give states greater flexibility in deciding how to measure school performance. In exchange, the states must adopt certain education reforms.

As The Washington Post’s Lyndsey Layton reported last week, states are primarily interested in exemptions from a provision of the law that calls for every student to be proficient in math and reading by 2014, with the risk of escalating sanctions for schools that do not comply.

In Virginia, 40 percent of schools were considered failing under the law last year. State officials said last week that they intended to seek a waiver. McDonnell, who heads the Republican Governors Association, endorsed that move at a national education forum in New York City on Monday, and again on WTOP Tuesday.

“Education is primarily the responsibility of parents, the states and the local school boards, not the federal government,” he told WTOP, “and so I think this is a step in the right direction.”