A leading Republican politician in Indiana has resigned following reports that at least one sexually explicit video had been sent from his mobile phone – after he claimed it had been stolen.

Jud McMillin, who had been the second-highest ranked official in the Indiana House of Representatives, quit abruptly on Tuesday, according to the Indianapolis Star.

The newspaper claims that Mr McMillin, a rising star in the state's Republican Party, tendered his resignation after sending a text message to several contacts to say: “My phone was stolen in Canada and out of my control for about 24 hours. I have just been able to reactivate it under my control. Please disregard any messages you received recently. I am truly sorry for anything offensive you may have received.”

He has not yet responded to requests for comment, but issued a written statement in which he said he had decided to "focus on his family".

"The time is right for me to pass the torch and spend more time with my family," the Star reported. "Now I want to focus all of my attention on making my family's world a better place."

Neither the House or Mr McMillin formally revealed the nature of the "offensive" material, the Indianapolis Business Journal reported.

House Speaker Brian Bosma accepted Mr McMillin’s resignation, saying in a written statement that he was “thankful for Rep. McMillin’s service to our state, and we fully support his decision to step down in order to focus on his family.”

His resignation comes less than a year after the caucus elected him to be the majority floor leader – and he was widely expected to seek the speaker’s job. House Republicans plan to call a caucus in the coming days to fill the majority floor leader position.