A meeting between Donald Trump Jr. and a Russian lawyer in June 2016 was also attended by a Russian-American lobbyist who was a former Soviet counter-intelligence officer, NBC News reported on Friday.
President Trump continued to downplay the issue, saying that "nothing happened" as a result of the meeting.
Trump Jr. on Tuesday morning posted a series of emails between himself and Rob Goldstone, a music publicist who contacted Trump Jr. and told him about an opportunity to receive potentially damaging information about Clinton as part of a Russian government effort to help his father's campaign.
Grassley's decision was co-signed by the committee's top Democrat, Sen.
Grassley, Iowa's senior Republican senator, serves as chairman of the judiciary committee - one of several committees conducting investigations into possible coordination between the Trump campaign and Russian government to influence the 2016 presidential election.
The letter questioned how Natalia Veselnitskaya - the Russian lawyer who met with the Trump campaign last summer - was allowed to travel to the United States, despite past attempts where she was denied a USA visa. Dianne Feinstein, D-Calif., and Donald Trump Jr could testify as early as next week.More news: Microsoft to Offer Skype for Business in New BMW 5 Series
Trump said in comments released by the White House on Thursday that he would invite Putin to the White House but added that now was not the right time for that.
Trump also disputed that Putin ever claimed Trump had accepted his denials, insisting Putin "didn't say that".
The president's attorney, Jay Sekulow, said in an interview with NBC's "Today" that Trump Jr. did not violate any laws by accepting the meeting.
Sekulow said the president was not being investigated by Mueller.
Working in consultation with the White House to select a nominee, including an hour-long meeting with Trump and several phone calls, Grassley said in June he was pleased with the selection process.
"In retrospect I probably would have done things a little differently", Trump Jr. said. They have insisted that they did not collude with Russian Federation during the 2016 campaign.