Tillerson's remarks come as the Trump administration is conducting an interagency review of its Cuba policy
, which is expected to result in a roll back of some Obama-era changes.
President Donald Trump is expected to reveal his administration's new policy toward Cuba in a speech in Miami on Friday
, two US officials told CNN over the weekend.
In his testimony, Tillerson described a dichotomy between the "sunny" and "dark" sides of the US-Cuba relationship -- the first of which promotes economic development and access to information in Cuba, while the latter provides revenue for the authoritarian regime, which inherently benefits from any influx of cash on the communist island.
"If we're going to sustain the sunny side of the relationship," Tillerson insisted, "Cuba must -- absolutely must -- begin to address its human rights challenges."
"Within that sunny side of the relationship there are troubling elements to us that bring the relationship into conflict with existing statute obligations," Tillerson added, referring to a series of US laws passed to economically isolate the country.
"As we're developing these business relationships, and as we're enjoying the benefits on the economic and development side," Tillerson asked, "are we inadvertently or directly providing support to the regime? Our view is, we are."
"We think we have achieved very little in terms of changing the behavior of the regime in Cuba and its treatment of people," Tillerson later added. "And it has little incentive today to change that."
In a second hearing Tuesday afternoon, Democratic Vermont Sen. Patrick Leahy questioned why the administration chose to single out Cuba for its human rights record, while allying closely with other authoritarian governments.
"The President has gone out of his way to praise the leaders of very repressive regimes in Saudi Arabia, Egypt, Russia, Turkey, the Philippines," Leahy said. "But now I see that the White House wants to change our relations -- which have finally begun to improve -- with Cuba?"