Massie, who is an outspoken critic of President Donald Trump, accuses Hegseth of, among other things, participating in starting wars without congressional approval.
Impeaching Hegseth is considered to have weak support among Republicans, who have the majority in the House of Representatives.
But the attempts were halted when Speaker Johnson unexpectedly announced that Thursday's votes were being canceled - and thus Massie's proposal. The House of Representatives will not reconvene until after the so-called midterm elections on November 3.
Johnson at the same time defended Hegseth and called Massie's impeachment attempt "ridiculous."
