WASHINGTON — An Iraqi man who worked as a translator for the American military before moving to the United States in 2009 was arrested on Thursday in Texas by F.B.I. agents who say he pledged allegiance to the leader of the Islamic State last year and misled them about his travels to Syria.

The Justice Department said that the man, Bilal Abood, 37, a naturalized American citizen who lives in Mesquite, a Dallas suburb, was charged with lying to an agent after he denied last month that he had pledged loyalty to Abu Bakr al-Baghdadi, the head of the self-described Islamic State.

An examination of his computer, seized in July under a search warrant, showed that on June 19 he had written on Twitter, “I pledge obedience to the Caliphate Abu Bakr al-Baghdadi,” officials said. The caliphate is the unified Muslim state that Mr. Baghdadi claims to have created, which is also known as ISIS or ISIL.

Officials said the timing of the arrest of Mr. Abood, who had been under F.B.I. scrutiny for more than two years, reflected increasing wariness about the possible threat posed by known devotees of the Islamic State inside the United States. The group has called on its followers to carry out attacks in its name, and two Islamic State supporters were shot dead by the police on May 3 in Garland, Tex., after they opened fire on a contest for Prophet Muhammad caricatures.