Sen. Marco RubioMarco Antonio RubioFive years after the Pulse nightclub massacre the fight for LGBTQ+ rights continues Rubio calls on Biden to 'forcefully' confront Iran over movement of war ships Bipartisan lawmakers want Biden to take tougher action on Nicaragua MORE (R-Fla.) on Tuesday said he will support the Republican presidential nominee, but he tried to avoid saying Donald TrumpDonald TrumpBiden prepares to confront Putin Biden aims to bolster troubled Turkey ties in first Erdoğan meeting Senate investigation of insurrection falls short MORE’s name.

"I'm going to support the Republican nominee," Rubio told CNN's "The Lead," saying his support would carry through "the entire process."

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"Well, I'm not voting for [Democratic front-runner] Hillary ClintonHillary Diane Rodham ClintonBiden prepares to confront Putin Ending the same-sex marriage wars Trump asks Biden to give Putin his 'warmest regards' MORE," Rubio added when pressed by host Jake Tapper.

Rubio said he was unsure whether he would attend the party's national convention in July but said his decision would not be "because of Donald Trump or in spite of Donald Trump."

Several prominent Republicans, including 2012 GOP nominee Mitt Romney and the Bush family, have indicated they won't attend. 

Rubio said he may go "if there is a role for me to play." 

Rubio argued he was compelled to support Trump, the presumptive GOP nominee, in light of others, such as Speaker Paul RyanPaul Davis RyanZaid Jilani: Paul Ryan worried about culture war distracting from issues 'that really concern him' The Memo: Marjorie Taylor Greene exposes GOP establishment's lack of power The Hill's 12:30 Report - Senators back in session after late-night hold-up MORE (R-Wis.), who caused waves last week by saying he wasn't ready to endorse the businessman. Ryan and Trump plan to meet Thursday on Capitol Hill.

"The difference between Speaker Ryan and myself is I ran for president. I signed a pledge," Rubio told CNN. "I said I would support the Republican nominee, and that's what I intend to do."

Still, Rubio argued that Trump's statements carry more weight now that he's the party's presumptive nominee, and he said he hoped Trump would "accept the gravity of that." Rubio has spoken out against Trump's remarks on foreign policy.

Rubio, who is of Cuban descent, was asked about Trump's Cinco de Mayo tweet of himself with a taco salad and whether it was enough to reach out to Hispanic voters.

"A tweet? Of course not," Rubio said. "After 11 months of this thing, I'm not surprised by anything that comes up on Twitter anymore."

Rubio denied that Sen. Ted CruzRafael (Ted) Edward CruzBiden tries to erase Trump's 'America First' on world stage Cotton, Pentagon chief tangle over diversity training in military GOP senators press Justice Department to compare protest arrests to Capitol riot MORE (R-Texas) reached out to him to discuss teaming up as Cruz's running mate following the Florida senator's exit from the race in mid-March after losing his home-state primary. CNN reported on efforts by the Cruz camp to reach out to Rubio.

Rubio said he spoke with Cruz the day after the Florida primary, but he said Cruz "didn't say a word about VP or anything of that nature." He called the story "unfortunate" and said the leaking of such information was a "classless move" — given that Cruz went on to pick Carly Fiorina as his running mate a week before suspending his campaign.

Rubio indicated in a statement Monday he had no interest in becoming Trump's running mate after the businessman acknowledged several phone conversations with Rubio since the senator dropped out of the race. 

Rubio argued that Trump would be best served by a running mate and aides "who fully embrace his campaign," which he reiterated Tuesday afternoon after Trump took a veiled swipe on Twitter, suggesting Rubio was never asked to fill the position. 

Rubio said Tuesday he planned to finish his term in the Senate at the end of this year and then return to life as a private citizen — and not to become a lobbyist or run for governor in two years. He said he didn't have "defined plans" after January.

— This post was updated at 4:51 p.m.