Five young American men under investigation in Pakistan for alleged terror links had established contact with a Taliban recruiter and have told FBI officials they were on a mission to be martyred, a Pakistani police official said. The five Muslim students were being questioned Saturday by local law enforcement and intelligence agencies in the eastern city of Lahore, where they were shifted in the morning, Sargodha town police chief Usman Anwar said. FBI agents, who have been granted access to the men, are trying to see if there is enough evidence to charge any of them with conspiracy to provide material support to a terrorist group, an American official and another person familiar with the case said Friday. They spoke on condition of anonymity because they were not authorized to discuss the investigation. The case has fanned fears that Americans and other Westerners - especially those of Pakistani descent - are traveling to Pakistan to join up with al-Qaida and other militant groups. It comes on the heels of charges against a Chicago man of Pakistani origin who is accused of surveying targets for the 2008 terrorist attacks in Mumbai, India. The main contact of the five men in Pakistan was a Taliban recruiter who went by the name "Saifullah," Anwar said. He would not give any more details about the recruiter or the nature of their contacts, but said Saifullah may have planned to take the men to Mianwali, a district near Pakistan's North West Frontier Province, a region where al-Qaida and the Taliban have proliferated. "Martyrdom was their mission. This is the same thing they told the FBI's legal assistance team," Anwar said. "They have said openly that they had come to be martyred." Pakistani police have said the five men wanted to join militants in Pakistan's northwest tribal areas before crossing into Afghanistan. The men are accused of using the social networking site Facebook and the Internet video site YouTube to try to connect with extremist groups in Pakistan. When they arrived in Pakistan, they allegedly took that effort to the street. They are alleged to have met representatives from the al-Qaida-linked Jaish-e-Mohammed militant group in the southeastern city of Hyderabad and from a related group, Jamaat-ud-Dawa, in Lahore, but were said to have been turned away because they were not trusted. Officials in Pakistan and the US expect the five, who are from the Washington, DC, area, to be deported back home. But Pakistan may hold them long enough for US prosecutors to prepare charges, and there was no immediate indication how long that might take. While Pakistani officials have said the men admitted trying to connect with militant groups, an FBI note sent to American lawmakers Thursday evening said the bureau had "no information linking them to terrorist organizations." That FBI note did not address whether the students attempted to join a terrorist group. Another possible charge - and one that could be more difficult to bring - would be conspiracy to maim or kill people overseas. Making that case would depend greatly on what the men say to FBI agents - and whether any evidence or incriminating statements gathered by Pakistani police would meet US legal standards. Statements made by Americans to police overseas can be used against them in a US trial if they weren't coerced. Another key source of evidence could be the men's computers, on which Pakistani police say they found maps of areas where terrorists operate. The men were reported missing by their families more than a week ago after one of them left behind a farewell video showing scenes of war and casualties and saying Muslims must be defended. Pakistani police detained them this week - along with one of their fathers - in Sargodha, a town in the eastern province of Punjab. One of the men being held is identified as an Egyptian American named Ramy Zamzam, a dental student at Howard University in Washington. The others were identified as Waqar Hussain, Aman Yemer, Ahmad Minni, Umar Farooq and his father, Khalid Farooq. Investigators are still trying to establish what role - if any - the father played in the men's alleged activities, officials said. Pakistani officials have given various spellings of their names. The FBI note said two of the young men are of Ethiopian descent, and two are of Pakistani descent. The note was provided by a congressional official on condition of anonymity because it was not public. Pakistan has many militant groups based on its territory, and the US has been pressing the government to crack down on extremism. Al-Qaida and Taliban militants are believed to be hiding in the lawless tribal belt near the Afghan border.