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updated 8:14 AM EDT, Thu October 2, 2014

Sen. Rand Paul, R-Kentucky, is considering a 2016 bid for the Republican presidential nomination.

STORY HIGHLIGHTS

Washington (CNN) -- Sen. Rand Paul said Wednesday that experts and government officials are downplaying the Ebola threat, and he speculated whether the U.S. may end up with a "whole ship full" of American soldiers infected with the virus.

In two interviews the Kentucky Republican and ophthalmologist suggested that the U.S. consider canceling flights from affected countries, and that the border with Mexico is not secure enough to keep infected individuals out.

How the Ebola virus spreads

Speaking to conservative talk radio host Laura Ingraham, Paul questioned whether the Obama administration should carry out its plan to send 3,000 troops to Ebola hot zones in Africa.

"You also have to be concerned about 3,000 soldiers getting back on a ship. Where is disease most transmittable? When you're in a very close confines on a ship, we all know about cruises and how they get these diarrhea viruses that are transmitted very easily," he said. "Can you imagine if a whole ship full of our soldiers catch Ebola?"

Your Ebola questions answered

At a Pentagon press conference, civilian officials said no decisions have been made about the procedures for troops returning to the U.S., even though some are already there, CNN Pentagon Correspondent Barbara Starr reported.

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Rand Paul plays up Ebola fears