Petitioner David H. McClain appeals the district court’s denial of his 28 U.S.C. § 2241 habeas corpus petition. The issue is whether the district court erroneously denied him credit on his federal sentence for time incarcerated. For reasons stated hereafter, we affirm in part and reverse in part the decision of the district court.

I.

On March 6, 1990, petitioner was arrested in Davidson County, Tennessee, on forgery charges and held because he was unable to make bond. He pled guilty in Davidson County Criminal Court to theft and was sentenced on August 21, 1990, to four years in prison.

While petitioner was serving that state sentence, on October 17, 1990, the United States Marshals Service requested that he be held on federal credit card fraud charges. Petitioner was then transferred to federal custody by writ of habeas corpus ad prose-quendum on January 4, 1991. On March 4, 1991, petitioner pled guilty in federal court to one count of credit card fraud. On July 1, 1991, while in federal custody awaiting sentence on the federal charge, petitioner was paroled by state authorities. He was sentenced on October 11, 1991, to twenty-one months imprisonment, to run concurrently with any state sentence, plus two years of supervised release, and was to be given credit for jail time served in federal custody. On November 1, 1991, the Marshals Service delivered petitioner to the Bureau of Prisons, who refused to grant him credit for time[*505] spent in custody prior to his sentencing on October 11, 1991. Petitioner’s release date from federal custody was projected to be April 19, 1993.

II.

Petitioner first argues that he is entitled to credit against his federal sentence for all time spent in federal custody.

18 U.S.C. § 3585(b) provides:

A defendant shall be given credit toward the service of a term of imprisonment for any time he has spent in official detention prior to the date the sentence commences—

(1) as a result of the offense for which the sentence was imposed; or

(2) as a result of any other charge for which the defendant was arrested after the commission of the offense for which the sentence was imposed;

that has not been credited against another sentence.

Specifically, petitioner claims that he is entitled to credit from March 6, 1990, the initial arrest date, or from January 4, 1991, the date he was taken into federal custody. Petitioner was serving a state sentence when he was transferred under a writ of habeas corpus ad prosequendum. The Bureau of Prisons determined that the time from January 4, 1991, to October 11, 1991, had been credited by the State of Tennessee against the state sentence, so it gave petitioner credit only for the time served after sentencing. The district court correctly concluded that the Attorney General, not the court, has the authority to compute sentence credits for time in detention prior to sentencing. United States v. Wilson, — U.S.—, 112 S.Ct. 1351, 117 L.Ed.2d 593 (1992). The district court may, however, grant petitioner relief under 28 U.S.C. § 2241. Wright v. United States Bd. of Parole, 557 F.2d 74, 77 (6th Cir.1977).

Petitioner argued before the district court that but for the federal charges, he would have been released by the Tennessee Department of Corrections, and thus the continued detention must be attributed to the federal charges. The district court, however, believed that this argument ignores the plain language of § 3585, which is intended to prevent double credit for detention incurred before a sentence actually begins. Accordingly, the district court held that the Attorney General is prohibited from granting petitioner credit for the time served from January 4, 1991, to October 11, 1991.

Petitioner further argues that because the federal judgment provides that the federal sentence is to run concurrently with the state sentence, he should receive presentencing credit. The government argues, however, that because petitioner was in federal custody on a writ of habeas corpus, he received credit on his state sentence for time spent in federal custody prior to the imposition of the sentence.

III.

We hold that petitioner should be given credit on the federal sentence for the time that he was on state parole, from July 1, 1991, until the date of his sentence, October 11, 1991. The federal government took custody from the state by virtue of the writ. However, once paroled he was in federal custody only because he was awaiting federal sentence. His release on parole from state charges essentially put him in exclusive federal custody. Therefore, the district court should have directed that the Attorney General credit petitioner with the additional time spent in custody after he was paroled.

Petitioner has been released from federal custody. However, his supervised release dates are affected by the erroneous computation. Thus, his claim is not moot.

The decision of the district court is REVERSED in part and this matter is REMANDED for further proceedings consistent with this opinion.