ADDISON, Tex. — Rick Perry, the former Texas governor whose 2012 campaign for the White House turned into a political disaster that left him humbled and weakened, announced Thursday that he would run for president again in 2016, exuding confidence in front of a crowd of veterans while making no specific reference to his first unsuccessful bid.

Mr. Perry is the latest candidate to enter a crowded field of Republican presidential contenders, declared and undeclared, several of whom have Texas ties and have overshadowed him in recent months, including Senator Ted Cruz and Jeb Bush, the brother of former President George W. Bush, Mr. Perry’s predecessor in the governor’s mansion.

“We are just a few good decisions away from unleashing economic growth, and reviving the American dream,” he told flag-waving supporters in a hangar at the municipal airport in this Dallas suburb. Striking a theme he is sure to repeat as he campaigns this weekend in Iowa, New Hampshire and South Carolina, he added: “It can be done because it has been done — in Texas.”