(CNN) President Donald Trump's former national security adviser, retired Gen. Michael Flynn, has refused a new request to appear as a witness before the Senate intelligence committee, a congressional source tells CNN.

Flynn first declined to comply with a Senate subpoena in May, asserting his Fifth Amendment rights. More recently, the committee has reiterated its request and Flynn has declined again, the source said.

The Senate intelligence committee has sought testimony from Flynn as part of its investigation into alleged Russian interference in the 2016 US elections, as well as whether Trump associates had any involvement. Flynn resigned from the White House in February amid controversy over his communications with the Russian ambassador to the US.

Reached by CNN, Flynn's lawyer Robert Kelner declined to comment.

Flynn has also been subpoenaed by the House intelligence committee, which is conducting a separate probe into Russia's election meddling. Flynn had offered to testify before both the Senate and House intelligence committees in exchange for immunity, but neither committee accepted the offer.

A committee source tells CNN that since the public subpoena for his business records, the House intelligence committee has not made additional requests for documents or testimony, but that does not preclude future requests.

In June, CNN reported that Flynn handed over more than 600 pages of documents to the Senate intelligence committee, including business records and personal documents "based on the narrowed requests from the committee." The documents were in response to two subpoenas that the committee sent to Flynn businesses after he invoked his Fifth Amendment rights.

Senate Intelligence Chairman Richard Burr, a North Carolina Republican, has said the committee has ruled out considering Flynn's request for immunity to testify before the committee.