Federal investigators on Thursday found a loaded gun that had been smuggled into the Manhattan jail where the financier Jeffrey Epstein hanged himself last summer while awaiting trial on sex-trafficking charges, officials said. The discovery of the gun at the jail, the Metropolitan Correctional Center, came amid a weeklong lockdown that began with a tip that a firearm might have been introduced" into the building, according to a statement from the federal Bureau of Prisons. The gun was found in one of the jail's housing units, the bureau said. The Metropolitan Correctional Center and other federal prisons across the United States have been dealing with rising levels of violence and other safety problems, including an influx of contraband. The problems have coincided with a push by the Trump administration, in its quest to shrink the federal government, to curtail prison hiring, according to a 2018 investigation by The New York Times. In at least one prison, The Times found, people regularly walked up to the double security fence in broad daylight, and, with no guards in sight, tossed weapons, drugs, cellphones and other items to inmates. But a gun is a rare and unique threat. The lockdown and ensuing search were part of the continuing fallout stemming from the suicide of Mr. Epstein in August. Lawyers for Mr. Epstein have challenged the New York City medical examiner's finding that his death was a suicide.