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Mr. Connolly and Rep. Frank Wolf, Virginia Republican, are sponsoring legislation that would shrink the airports board from 17 members to nine, and give Virginia control over a majority of the appointments.

The committee chairman, Rep. John Mica, Florida Republican, said Mr. Connolly makes “a pretty good case.” But D.C. Delegate Eleanor Holmes Norton opposed what she said would amount to a takeover of the board by Virginia. She noted a recent compromise last year that expanded the board by four members and gave Virginia two of those slots.

She said she is sympathetic to the notion that Virginia wants to control its own affairs but said the District needs a say in how the airports used by its residents are managed.

“You want to talk about home rule? Let’s start with the District of Columbia. Then we’ll get to Virginia,” Ms. Norton said.