MEXICO CITY (Reuters) - Mexico has ordered the arrest of an outgoing state governor in the ruling party suspected of corruption, as well as one of his opposition contemporaries, the government said on Wednesday, as it seeks to quell public discontent about its record on graft.

Attorney General Arely Gomez said an arrest warrant was issued for outgoing Veracruz governor Javier Duarte on suspicion of involvement in organized crime and money laundering, just a few days after he took a leave of absence from the job.

The government also said it was seeking the arrest of Guillermo Padres, a member of the opposition center-right National Action Party battling allegations of corruption who governed the northwestern state of Sonora until last year.

President Enrique Pena Nieto's credibility has been damaged by accusations he has been soft on corruption and he himself became embroiled in an embarrassing conflict-of-interest scandal in 2014 that included his wife and then-finance minister.

Duarte, a member of Pena Nieto's Institutional Revolutionary Party (PRI), has become the most public face of the government's inability to silence its critics over graft, and party insiders have for weeks said that his arrest was imminent.

Duarte's whereabouts are currently unknown, and Interior Minister Miguel Angel Osorio Chong stressed he would be caught.

"It's down to us to capture (him) now," he told local radio. "We've done it with others, and we'll do it with the two they're looking for now, the one from Sonora and the one from Veracruz."

Attorney General Gomez was speaking at a news conference in the city of Acapulco when she announced the arrest order for Duarte, adding that warrants were also issued for nine of his associates. Two of them were arrested on Tuesday, she said.

Duarte, who presided over a spike in gang violence and kidnappings in Veracruz, as well a doubling of state debt, has denied any wrongdoing. He could not be reached for comment.

Duarte has not appeared in public since giving an interview on Mexican television last week. On Wednesday evening, the PRI said it would proceed with the process of expelling Duarte, calling him to testify before its justice committee next week.

Two government officials said the attorney general's office was seeking Padres' arrest, but could not specify the charges.

This month, the PAN provisionally stripped Padres of his party rights, citing outstanding investigations into suspected corruption. Padres could not immediately be reached for comment.

(Reporting by Anahi Rama and Natalie Schachar; Writing by Frank Jack Daniel; Editing by Dave Graham and Richard Chang)