UPDATE 1-Tillerson raises prospect of Venezuela military ouster of Maduro

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AUSTIN, Texas, Feb 1 (Reuters) - U.S. Secretary of State Rex Tillerson on Thursday raised the prospect that the Venezuelan military could decide to oust President Nicolas Maduro but said he did not know whether that would happen.

In a speech at the University of Texas ahead of five-nation Latin America tour, Tillerson insisted the Trump administration was not advocating "regime change" in Venezuela but said it would be "easiest" if Maduro chose to leave power on his own.

Tillerson predicted there would be change of some kind in Venezuela and said the United States, which has had steadily worsening relations with the country's Socialist government, wanted it to be a peaceful one.

Maduro, whose approval ratings are low amid a collapsing economy, runaway inflation and rising malnutrition in the oil-producing country, is seeking re-election in a vote that must be held by the end of April.

We have not advocated for regime change or removal of President Maduro. We have advocated that they return to the constitution, Tillerson said when asked during a question-and-answer session whether the removal of Maduro was necessary or the United States would play a role in it.

However, he then suggested the possibility that internal forces might take action, though he offered no evidence the United States had intelligence backing the notion that the military might turn against Maduro.

"In the history of Venezuela and in fact the history in other Latin America and South American countries, often times, it is the military that handles that," Tillerson said.

"When things are so bad that the military leadership realizes that it just can't serve the citizens anymore, they will manage a peaceful transition," he said. But he added that, "Whether that will be the case here or not, I do not know."

The United States and other Western governments accuse as Maduro's government of violating political and human rights in Venezuela and have imposed economic sanctions. Critics at home say Maduro, who succeeded Hugo Chavez in 2013, has wrecked the economy and skewed the election system to perpetuate power for his Socialist Party.

Maduro's government, which is allied with Cuba's Communist leadership, says it is fighting a U.S.-led right-wing conspiracy determined to end socialism in Latin America, hobble Venezuela's economy, and steal its oil wealth.

The Venezuelan government did not respond immediately to a request for comment.

"Maduro should get back to his constitution and follow it," Tillerson said. "And then, if he is not re-elected by the people, so be it."

"Then, if the kitchen gets a little too hot for him, I am sure that he got some friends over in Cuba that could give him a nice hacienda on the beach and he could have a nice life over there." (Reporting By Matt Spetalnick, David Brunnstrom and Jon Herskovitz, writing by Matt Spetalnick; Editing by Alistair Bell)