Robert Mueller, the special counsel overseeing the Russia election meddling probe, is zeroing in on the initial response given by the US president's son over a controversial meeting with a Russian lawyer, the New York Times reported Wednesday.

Donald Trump Jr issued an initial statement last July saying the meeting, held in Trump Tower in 2016, was set up to discuss a Russian adoption policy.

The statement was reportedly crafted with direct input from President Donald Trump.

But Trump Jr later released a set of pre-meeting emails in which he expressed interest in meeting with the lawyer, Natalia Veselnitskaya, in order to obtain what he was told would be damaging information on Democratic presidential candidate Hillary Clinton.