In a rare display of bipartisanship, the House approved a bill on Tuesday supporting the expansion of charter schools, the first part of a legislative package planned by Republicans to carry out a piecemeal rewrite of the main federal law on public education, No Child Left Behind.

The bill, passed Tuesday by a vote of 365 to 54, tweaks an existing federal grant program that provides start-up money for new charter schools — currently about $250 million— and adds some quality control provisions.

It had the support of charter operators as well as civil rights and school improvement groups. If passed by the Senate, it would replace the charter school provisions of No Child Left Behind, the sprawling school accountability law that President George W. Bush signed in 2002.

“This is an important first step in our efforts to improve current elementary and secondary