US Vice-President Mike Pence says sanctions will remain on Venezuela despite the release of a US prisoner and his wife on Saturday.
Joshua Holt and his Venezuelan wife Thamy arrived in the US accompanied by Senator Bob Corker, who helped negotiate their release.
Mr Holt later met President Donald Trump at the White House.
Mr Holt and his wife had been imprisoned in Venezuela for two years on charges of concealing weapons.
"Very glad that Josh Holt is now back home with his family - where he has always belonged," Mr Pence wrote in a tweet. "Sanctions continue until democracy returns to Venezuela."
The couple were detained in 2016 at her family's house in the capital Caracas while waiting for US visas, and accused of hiding weapons. Both were jailed for two years.
Mr Corker had held talks on Friday with Venezuelan President Nicolás Maduro.
The US senator shared a picture of himself with the couple after their release, adding: "We are on our way home."
I am pleased to join Senator Hatch and President Trump in announcing the release of Josh and Thamy Holt. We are on our way home. pic.twitter.com/0Ku2pzwOYL— Senator Bob Corker (@SenBobCorker) May 26, 2018
Sitting alongside Mr Holt in the Oval Office, President Trump told him he had been "incredibly brave."
"It's amazing that you were able to take it... that was a tough situation," he said with Mr Holt's family looking on.
Mr Holt said he was "overwhelmed" to be back home.
"I'm just so grateful for what you guys have done, and for thinking about me, and caring about me, just a normal person," he added. "It really touches me."
A spokesman for Mr Maduro said the couple's release was a "gesture" aimed at improving dialogue between Venezuela and the US.
Mr Maduro was re-elected to a six-year term last week, but Washington has refused to recognise the outcome. The election was marred by an opposition boycott and allegations of vote-rigging.
The US had previously accused Venezuela of using Mr Holt as a bargaining chip towards changing Washington's sanctions policy on the country.
Venezuela has not discussed the nature of the talks with Mr Corker, the chairman of the Senate Foreign Relations Committee, but said they were "good news for the Venezuelan people".
Good news about the release of the American hostage from Venezuela. Should be landing in D.C. this evening and be in the White House, with his family, at about 7:00 P.M. The great people of Utah will be very happy!— Donald J. Trump (@realDonaldTrump) May 26, 2018
Looking forward to seeing Joshua Holt this evening in the White House. The great people of Utah are Celebrating!— Donald J. Trump (@realDonaldTrump) May 26, 2018
Mr Holt is a former Mormon missionary from Utah who had travelled to Caracas in June 2016 to marry his Venezuelan girlfriend, Thamy Caleno.
She is also a Mormon and the couple intended that Ms Caleno and her children would move with Mr Holt to the US following the marriage, but they were arrested instead.
Utah Senator Orrin Hatch, who said he had worked with two presidential administrations and various contacts, including President Maduro, on the release, said that he "could not be more honoured to be able to reunite Josh with his sweet, long-suffering family".
Mr Maduro has frequently accused the US of trying to overthrow him and the US has tightened sanctions recently. Only on Tuesday, he expelled the senior US representative in the country, Todd Robinson.
Venezuela is five years into an economic crisis, suffering from hyperinflation and severe shortages in food and medicine.
Turnout was low in last Sunday's election, boycotted by much of the opposition. Mr Maduro was credited with winning 68% of the vote.