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Story highlights

House Speaker Paul Ryan said Thursday Donald Trump should not have made comments suggesting there would be riots at their party's convention this summer

Ryan's remarks comes as his party's presidential front-runner collects more delegates

(CNN) —  

House Speaker Paul Ryan Thursday sharply condemned Donald Trump’s suggestion that there could be riots at the GOP convention if he’s not the presidential nominee, saying “nobody should say such things in my opinion because to even address or hint at violence is unacceptable.”

The Wisconsin Republican was asked at his weekly press conference about Trump’s warning in comments he made to CNN Wednesday that there would be “riots” if he were denied the nomination at an open convention.

Ryan has previously criticized the businessman’s proposal to ban Muslims and his failure to denounce the Ku Klux Klan.

RELATED: Donald Trump on brokered convention: ‘I think you’d have riots’

The 2012 Republican vice president nominee acknowledged that an open convention to select the Republican party’s presidential nominee is “more likely” now, but again ruled out seeking the GOP nomination for himself.

Ryan said that he only learned after he was sworn in as speaker that one of his duties was to chair the party’s convention and he stressed elected delegates following party rules should govern that process.

“This is more likely to become an open convention than we thought before, so we’re getting our minds around the idea that this could very well become a reality, and therefore those of us that are involved in the convention need to respect that,” Ryan said.

Ryan stood by his commitment that he won’t endorse any presidential candidate because of his position at the convention.

But pressed on whether he will need to “denounce” Trump’s candidacy altogether, Ryan said, “I do not believe I will have to do that. This is a democratic primary process. The Republican primary voter is going to make this decision on who our nominee is going to be.”

Ryan declined to comment on efforts by those Republicans in the “Never Trump” camp to form a third party to challenge Trump in the November election.

Some Republican leaders, including former House Speaker John Boehner, are floating Ryan’s name as an alternative nominee to Donald Trump, but again on Thursday he said he had no interest in the position.

“I saw Boehner last night and told him to ‘knock it off,’” Ryan said, and added, “it’s not going to be me. It should be someone running for president. I made a decision over a year ago not to run for president.”

RELATED: Conservative leaders gather to plot against Donald Trump