In an interview with CNN, Ryan downplayed concerns voiced by a growing number of GOP lawmakers who are eager to skip what could be a messy and controversial convention so they can instead worry about their own re-election fights back home.
"If you were planning on going to the convention, you should go," Ryan said in the Capitol. "It could be a great historical exercise. I mean, it could be something you'll remember the rest of your life, so I would go if I were, if I had a chance to go."
Asked about concerns from GOP lawmakers about being tied too closely to their nominee, Ryan said: "I think that we should go. This is our convention making our nominee, so I think everybody should participate."
The comments from Ryan -- who also serves as chairman of the Republican National Convention -- represent some of the strongest remarks he's made yet in calling for unity behind the GOP ticket. Yet he also rebuffed Donald Trump's criticism of the delegate selection process that the GOP front-runner has said is rigged.
"The rules are the rules," Ryan said.
And in the interview, Ryan firmly kept the door open to running for president in a future election cycle, even as he again insisted he wouldn't be the nominee in 2016.
Amid the increasingly personal feud between Trump and Ted Cruz, many Republican lawmakers want nothing do with what could be a mess in Cleveland. Moreover, Ohio Gov. John Kasich is trying to win the nomination by appealing to win over the 1,237 delegates if the fight goes to a second round of balloting. Trump has warned there could be "riots" if he's denied the nomination in Cleveland.
Several senators up for reelection -- namely Kelly Ayotte of New Hampshire, Mark Kirk of Illinois, Richard Burr of North Carolina and even the party's 2008 standard-bearer, John McCain of Arizona -- are signaling they will skip the convention. A number of House lawmakers are making similar warnings, including Rep. Mick Mulvaney of South Carolina. And even former Florida Gov. Jeb Bush, who lost his bid for the nomination this year, told CNN last week he would skip the convention.
Ryan, who emphatically said last week that he would not accept the party's GOP nomination even if delegates selected him in Cleveland, said the party needed to put its differences aside ahead of a crucial fall campaign.
"I'm not going to be skipping it," Ryan said. "People will make the decision on what they want to do. If you're a delegate, then they better not skip it."
'The rules are the rules'
Even as Ryan urged the party to get behind the eventual nominee, he made his most forceful comments yet over Trump's concerns over the GOP process for selecting delegates.
"I think the rules are the rules," Ryan said. "And people know the rules going into it, and we are going to follow the book by the rules and that is exactly how this convention is going to be run."
Echoing his fellow Wisconsinite, Republican National Committee Chairman Reince Priebus, Ryan said: "All of the candidates coming into this convention and coming into this campaign knew the rules ahead of time."
Ryan said he has yet to fully think through how a contested convention would play out, saying a candidate could clinch the nomination before the battle in Cleveland.
"It very well may be that somebody gets 1,237 delegates before the convention and then this whole open convention question is closed," Ryan said. "But maybe we will have an open convention. If we do, we will deal with the situation as it arises."
Yet he rejected Trump's suggestions that a candidate who wins the most delegates should get the nomination -- even if it fails to reach the majority threshold of 1,237.
"The rules are the rules," Ryan said. "We're just going to follow the rule book and let the delegates make their decisions on how this goes forward."
Ryan doesn't rule out presidential run -- for next cycle
Last week, Ryan insisted he would not be the GOP's nominee this cycle, no matter what. In the CNN interview, he reiterated that only a candidate who has run for president should be the nominee.
But asked if he's foreclosed a run for president sometime in the future, Ryan said: "Well no, but I don't think that far down the road. I made a decision in this cycle for 2016 not to run for president."
Ryan, the party's 2012 vice presidential candidate, said he turned down a run in 2016 because he wanted to have a "balanced family life" and focus instead on his job as chairman of the tax-writing Ways and Means Committee, a position he held until he was unexpectedly elevated to speaker last fall.
"I thought I could make a huge difference and still have the kind of balanced life family that I enjoy at this stage in my life and that's why I didn't run for president," Ryan said. "But also because there are a lot of good people running."