President Trump Donald John TrumpOmar fires back at Trump over rally remarks: 'This is my country' Pelosi: Trump hurrying to fill SCOTUS seat so he can repeal ObamaCare Trump mocks Biden appearance, mask use ahead of first debate MORE’s lawyer Rudy Giuliani made up the Sept. 1 deadline he said special counsel Robert Mueller Robert (Bob) MuellerCNN's Toobin warns McCabe is in 'perilous condition' with emboldened Trump CNN anchor rips Trump over Stone while evoking Clinton-Lynch tarmac meeting The Hill's 12:30 Report: New Hampshire fallout MORE had placed on Mueller's investigation into whether Trump obstructed the Russia investigation, a source familiar with the investigation told Reuters.

The source called the deadline “entirely made up” and “another apparent effort to pressure the special counsel to hasten the end of his work,” Reuters reported.

The source went on to say that Mueller will wrap up the probe when “he thinks he's turned over every rock.”

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“He’ll wrap it up when he thinks he’s turned over every rock, and when that is will depend on how cooperative witnesses, persons of interest and maybe even some targets are, if any of those emerge, and on what new evidence he finds, not on some arbitrary, first-of-the-month deadline one of the president’s attorneys cooks up,” the source said.

On Sunday, The New York Times reported that Giuliani said Mueller intends to end his investigation into whether Trump obstructed the investigation into Russia's election meddling and whether there was collusion with the Trump campaign by Sept. 1.

According to Giuliani, the special counsel had provided his timeline for the investigation a few weeks ago during negotiations over whether the president would be willing to sit down with Mueller’s team for an interview.

The Washington Post, which spoke with Giuliani later on Sunday, reported that Mueller said he could end the investigation by September if Trump agreed to be interviewed.

Giuliani’s announcement of a deadline was seen as an effort to publicly pressure Mueller as Trump’s lawyers negotiate with his team about the potential interview.