Sen. Tom Cotton downplayed rumors that he'll run for president in 2024 ahead of his Thursday speech at the Republican National Convention.

"My name is on the ticket right now in Arkansas," Cotton, R-Ark., told "Mornings with Maria" on Wednesday. "I hope the people of Arkansas will trust me with another six years in the United States Senate."

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Cotton's July trip to New Hampshire – the state that for a century has held the first primary in the race for the White House  – sparked more speculation that the veteran Army infantry officer who served in the Afghanistan and Iraq wars may have his own national ambitions in 2024.

Republican Sen. Tom Cotton of Arkansas headlines a meet and greet with GOP activists at the Trump re-election campaign's New Hampshire headquarters, in Manchester, N.H. on July 31, 2020

"New Hampshire is also a critical swing state," Cotton said on Wednesday. "Remember, President Trump only lost it by a couple thousand votes in 2016, and we have competitive Senate races there. That's what I was doing in New Hampshire, as well as states like Tennessee, and I'm going to be traveling to Georgia next week to campaign as well."

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Cotton is among a handful of reported 2024 contenders who secured a speaking slot at the 2020 GOP convention. Others include former Ambassador to the United Nations Nikki Haley and Sen. Tim Scott, R-S.C.

Fox News' Paul Steinhauser contributed to this report.