WASHINGTON — The Justice Department has begun receiving information obtained by Rudolph W. Giuliani, President Trump’s personal lawyer, from Ukraine about former Vice President Joseph R. Biden Jr. and his son, Senator Lindsey Graham said on Sunday.

Mr. Graham, a South Carolina Republican who is the chairman of the Judiciary Committee and a vocal Trump ally, said Attorney General William P. Barr told him in a telephone call early Sunday morning that the department was “receiving information coming out” of Ukraine delivered by Mr. Giuliani.

“He told me that they have created a process that Rudy could give information and they would see if it’s verified,” Mr. Graham said on CBS’s “Face the Nation.”

A spokeswoman for the Justice Department declined to comment on Mr. Graham’s assertion. The department has previously taken steps to distance itself from Mr. Giuliani, and in September, it said Mr. Barr had “not discussed anything relating to Ukraine” with Mr. Giuliani.