Feinstein, D-Calif., and McCain, R-Ariz., released a joint statement with Denis McDonough, the White House chief of staff, who joined them on the tour Friday.
They praised those working at Guantanamo for keeping the remaining 166 detainees confined in "a safe and respectful way."
"We continue to believe that it is in our national interest to end detention at Guantanamo, with a safe and orderly transition of the detainees to other locations," the statement said. "We intend to work, with a plan by Congress and the Administration together, to take the steps necessary to make that happen."
President Barack Obama and McCain, the Republican presidential nominee in 2008, both promised to close Guantanamo during the campaign. After Obama submitted a plan, McCain criticized it, saying he had been unable to satisfy Congress.
The statement did not mention the ongoing hunger strike. There are currently 104 detainees on strike with 41 being force-fed, The Miami Herald reported.
Military authorities have asked for an increase in personnel to cope with the strike.
Feinstein is chairwoman of the Senate Select Committee on Intelligence. McCain is the ranking member of the Senate Committee on Armed Services.