A group of five Republican senators wrote to Tillerson, requesting the US declare Cuban diplomats unwelcome and shutter the embassy in Cuba, which the US opened near the end of former President Barack Obama's second term. US government officials have said
State Department employees in the Havana embassy were subject to mysterious "acoustic" attacks that led to serious health problems.
Tillerson addressed the concern, but did not specify what would happen.
"It's a very serious issue with respect to the harm that certain individuals have suffered," Tillerson said. "We've brought some of those people home. It's under review."
Obama eased the decades-long blockade on Cuba and sought to restore diplomatic ties between the two countries. After taking office, President Donald Trump said he was "canceling" the deal with Cuba and would return the US to a more adversarial posture with the island nation to spur it to do more to honor human rights.
In June, Trump unveiled
new restrictions on travel and business with Cuba.
Before Trump's announcement, Tillerson said he believed
Obama's approach had benefited the Cuban government without changing its behavior or the country's human rights situation.
Paris climate accord
The White House said Saturday the administration still intended
to withdraw the US from the Paris climate agreement after a European official told reporters the US appeared to be softening its stance.
Two of the Trump administration's top officials reiterated Sunday that Trump intended to withdraw from the agreement, unless the US could make changes to it.
Tillerson, in his CBS interview, said National Economic Council Director Gary Cohn was leading the administration's effort on the landmark agreement.
"Look, we are willing to work with partners in the Paris climate accord," Tillerson said of Trump's position.
He said the United States' voluntary commitment to the deal, which almost every other nation signed onto, was "really out of balance" relative to other economies. However, he said the US was willing and ready to stay in the deal if it established new terms.
"We want to be productive," Tillerson said, adding later, "Under the right conditions, the President said he's open to finding those conditions where we can remain engaged with others."
Trump's national security adviser H.R. McMaster, speaking on ABC's "This Week," said the US would "certainly" stay in the deal if it got an agreement that benefited the US, but the administration's current stance was to exit the deal.
"What the President has said is that we are withdrawing from the Paris Accord," McMaster said.