MEMORANDUM

Federal prisoner Anthony Leon Green-hill appeals pro se from the district court’s judgment dismissing his 28 U.S.C. § 2241 petition. We have jurisdiction pursuant to 28 U.S.C. § 2253 , and we affirm.

Greenhill contends that prison officials have been retaliating against him by mishandling his special/legal mail and that this constitutes an additional and unconstitutional restraint warranting habeas relief. He further argues that he is entitled to an evidentiary hearing on this claim. The appropriate remedy for Greenhill’s claim, which relates to the conditions of his confinement, lies in a civil rights action under Bivens v. Six Unknown Named Agents, 403 U.S. 388 , 91 S.Ct. 1999 , 29 L.Ed.2d 619 (1971), and the First Amendment. See Preiser v. Rodriguez, 411 U.S. 475, 498-99 , 93 S.Ct. 1827 , 36 L.Ed.2d 439 (1973) (holding that habeas relief applies when a prisoner challenges the fact or duration of his confinement, and a § 1983 action is the proper remedy for a constitutional violation relating to the conditions of prison life); Tucker v. Carlson, 925 F.2d 330, 331-32 (9th Cir.1991) (holding that a feder al prisoner challenging the execution of his sentence must bring a § 2241 habeas petition, whereas a prisoner complaining of civil rights violations must bring a Bivens action). Moreover, because the record conclusively shows that Greenhill is not entitled to § 2241 habeas relief, the district court did not abuse its discretion by failing to hold an evidentiary hearing. See Anderson v. United States, 898 F.2d 751, 753 (9th Cir.1990) (per curiam).

Greenhill also contends that the district judge did not have all of the necessary evidence before him when determining whether to dismiss the petition because the magistrate judge did not allow Green-hill’s “Appendix Addendum” to be filed. Greenhill has not met his burden of showing that the magistrate judge abused his discretion by rejecting the document on the basis that it failed to comply with the local rules. See Delange v. Dutra Const. Co., 183 F.3d 916 , 919 n. 2 (9th Cir.1999) (per curiam) (stating that district courts “ ‘have broad discretion in interpreting and applying their local rules’ ”) (quoting Miranda v. Southern Pac. Transp., 710 F.2d 516 , 521 (9th Cir.1983)).

Further, the district court properly dismissed the action with prejudice after noting the deficiencies of Greenhill’s § 2241 petition and giving him multiple opportunities to properly allege a Bivens action. See McHenry v. Renne, 84 F.3d 1172, 1177-80 (9th Cir.1996) (affirming dismissal with prejudice of civil rights complaint for repeated failures to corrected noted pleading shortcomings).

AFFIRMED.

This disposition is not appropriate for publication and except as provided by 9th Cir. R. 36-3.