Rep. Duncan Hunter on Tuesday asked Congress to evaluate whether enough states have officially called for a constitutional convention to propose a balanced budget amendment — marking the next step toward what could be an historic gathering.

Mr. Hunter, California Republican, said Congress should take stock of where things stand after Michigan last week approved an official call for a balanced budget amendment convention. According to some analysts, Michigan’s move makes it the 34th state to request a convention.

The final decision is up to Congress.

“It is my belief that the House should lead an effort to ascertain whether 34 states have voted affirmatively,” Mr. Hunter said in a letter to House Speaker John A. Boehner.

“A balanced budget amendment is long overdue and remains an effective tool to address runaway spending and deficits,” he wrote. “With the recent decision by Michigan lawmakers, it is important that the House — and those of us who support a balanced budget amendment — determine whether the necessary number of states have acted and the appropriate role of Congress should this be the case.”

Article V of the Constitution lays out two different ways for amendments to be proposed. The usual way, which has been the case for all 27 amendments so far, involves two-thirds of each house of Congress approving a resolution proposing an amendment. But the Constitution also says if two-thirds of state legislatures demand a convention, Congress shall convene one for the purpose of considering amendments.