"We respect any decision taken by him," Patricio Melero, head of the Independent Democratic Union, said at news conference in the port city of Valparaiso.
"Once he knew of this illness that is troubling him, and taking into consideration the opinion of doctors, he was brave to make this decision that puts the interest of the country above anything else," Melero said.
Party leaders will meet Thursday to pick a replacement for Longueira, an industrial engineer by training and a career politician who was close to Pinochet.
"This was such a surprising event. It wasn't considered under any political scenario because the campaign is on its final stretch. This is a crisis for the right-wing coalition," said Guillermo Holzmann, a political science professor at the Universidad de Valparaiso.
"This political crisis gives Bachelet an important electoral advantage," Holzmann said.
Bachelet, who ended her 2006-10 presidency with high popularity ratings, is campaigning on promises to use a second term to fight Chile's vast income inequality, change the Pinochet-era constitution and reform taxes and education.
"This has shocked me for many reasons, but above all as a human being," Bachelet said after hearing of Longueira's decision.
___
Associated Press writer Luis Andres Henao in Santiago, Chile, contributed to this report.
