The five were arrested in Sargodha, south of Islamabad, at the home of a member of the banned militant group Jaish-e-Mohammad, Pakistani district police chief Usman Anwar told AFP Wednesday.
Pakistani officials said the men were two Yemenis, one Egyptian, one Swede and a Pakistani-American. Muslim leaders in Washington said the men had been living in northern Virginia, close to the US capital, with their families until they disappeared last month.
An official at the Pakistani embassy in Washington said they are "all of US origin," but Federal Bureau of Investigations officials gave no confirmation of their nationalities.
The Swedish foreign ministry had no information about the arrests as of Wednesday night.
“The embassy is working to check out the information to see if it's true,” foreign ministry spokesperson André Mkandawire told the TT news agency.
Nor did Swedish security service Säpo have any details about the Swede's reported arrest.
“We're trying to figure out if it's true and what it could be about,” Säpo spokesperson Patrik Peter said to TT.
Sweden's ambassador in Islamabad, Ulrika Sundberg, told TT shortly after midnight local time that she also planned to investigate the matter.
The FBI said it was probing the case, in which one of the suspects made an extremist-style "farewell" video before leaving his home in the United States.
Officials from Washington, DC-based the Council on American Islamic Relations (CAIR) told reporters that the men's families contacted the organization after they went missing.
Nihad Awad, CAIR's executive director, did not give the men's names, ages or nationalities, but said he met on December 1 with their relatives.
Awad said the families brought along a video showing one of the five men delivering a "final statement," and which included war images and Koranic verses.
"It's like a farewell," he said of the 11-minute, English-language video that one of the families reportedly found in their home.
After viewing the video, CAIR contacted the FBI and turned over the footage and information about the missing men.
"The circumstances were so suspicious that we felt we had to bring it to the attention of the FBI," said Ibrahim Hooper, CAIR's national communications director.
That tip appears to be the first time authorities had been alerted to the men's activities, he added.
The FBI said it was working with families and local law enforcement to investigate the missing students.
"We are working with Pakistan authorities to determine their identities and the nature of their business there, if indeed these are the students who had gone missing," said Lindsey Godwin, an FBI spokeswoman.
Godwin said she could give no further details because "this is an ongoing investigation."
The official at the Pakistani embassy told AFP that the men entered the country through the southern city of Karachi on November 30 and went within days to the central province of Punjab.
They first went to the Punjabi capital, Lahore, before heading to Sargodha.
"We are still investigating the exact details," the official said on condition of anonymity.
US embassy spokesman Richard Snelsire said in Islamabad that he was aware of reports of the arrests, but had not received any information from Pakistani officials.
State Department spokesman Ian Kelly said he was unable to provide more details on any American connection in the arrests.
Asked more broadly about domestic radicalization, Secretary of State Hillary Clinton told CNN: "It's always been a concern."
"We have been well aware of the threats that we continue to face, along with friends and allies around the world. We know that much of the training and the direction for the terrorists comes from Pakistan and the border area with Afghanistan," Clinton added.
CAIR's Awad said the video referred to wars between the West and various Muslim nations.
"There were... images of conflict," he added, describing the video as "similar to videos we see on the Internet."
"It was generic, but you can draw your own conclusions."
The arrests came as a Pakistani-American, David Coleman Headley, pleaded not guilty Wednesday in a Chicago court to helping plan the deadly 2008 Mumbai attacks.
Headley, who changed his name from Daood Gilani in 2006, is accused of making trips to Mumbai over almost two years, even taking boat tours around the city's harbor to scope out landing sites for the attackers, who killed 166 people including six Americans.