Story highlights Trump Jr. has turned over documents to the committee and may still be asked to testify in public

The panel had invited him to attend a July hearing

(CNN) President Trump's eldest son, Donald Trump Jr., has agreed to sit down for a transcribed interview with the Senate judiciary committee, as investigators continue to dig into his attendance at a 2016 meeting where he was promised Russian dirt on the Clinton campaign.

The committee and Trump Jr. have agreed on a date to be interviewed by the panel in private, according to Taylor Foy, spokesman for committee Chairman Chuck Grassley, after Trump Jr.'s lawyers have been in discussions with the panel and turned over documents. Trump Jr. will be interviewed by senior committee staff, and senators could also attend, Foy said.

After the Senate judiciary committee invited him to attend a July hearing to testify in public, Trump Jr. instead cut a deal with the committee to avoid that session. It's unclear if he will eventually testify publicly, but committee leaders have said an open session with Trump Jr. is still on the table.

Grassley and the top Democrat on the panel, Dianne Feinstein of California, said in a statement Tuesday night that Trump Jr. agreed to a date for his interview shortly after telling the panel in late July he'd be willing to meet with them.

"This meeting will be conducted under the same terms as previously announced," the senators said in a statement.

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