"The latest scenes of carnage and mayhem sicken us all," Pence said during remarks from Panama.
Pence said the US condemned the "terror attack" and offered the nation's support and prayers to the people of Spain.
Pence delivered further comments later Thursday from Panama, saying the attack reminded the world about the threat that exists.
"Whoever is responsible should know the United States of America, along with our allies, will find and punish those responsible and drive the evil of radical Islamic terror from the face of the Earth," Pence said.
In his initial response on Twitter, Trump offered similar thoughts.
"The United States condemns the terror attack in Barcelona, Spain, and will do whatever is necessary to help. Be tough & strong, we love you!" Trump said.
He went on to reference
a debunked story he told on the campaign trail.
"Study what General Pershing of the United States did to terrorists when caught. There was no more Radical Islamic Terror for 35 years!" Trump said.
Several fact-checking sites have already run down the story.
Trump, speaking in South Carolina during the campaign, told a story
of Gen. John Pershing who, he said, shot 49 Muslim prisoners dead with bullets dipped in pigs' blood then ordered the one remaining prisoner to tell others what had happened. Trump said: "In 25 years, there wasn't a problem."
Snopes previously found
a lack of evidence the story, which has circulated online for years, and Politifact rated
Trump's comment as "pants on fire," saying the facts of the story were lacking and the point he was making was wrong.
Secretary of State Rex Tillerson offered US support to Spain, and said the US mission there was assisting American citizens affected by the attack.
"Terrorists around the world should know that the United States and our allies are resolved to find you and bring you to justice," Tillerson said.
Democrats and Republicans likewise took to Twitter to condemn the attacks and offer their thoughts.
"Pure evil in #Barcelona. We stand with the people of Spain, and send our prayers to the victims of this horrible terrorist attack," House Speaker Paul Ryan said.
House Minority Leader Nancy Pelosi said, "My thoughts are with all suffering after the terror attack in #Barcelona. Praying for the victims, their loved ones and the people of Spain."
"U.S. Senate community expresses condolences to the victims of the #Barcelona terrorist attack. America stands united w/ the people of Spain," Senate Majority Leader Mitch McConnell said.
Senate Minority Leader Chuck Schumer said, "My prayers are with #Barcelona after the terror attack. We stand firmly with you and against this awful violence."