Speaking at the National September 11 Memorial and Museum, Wray also made comments about the Las Vegas mass shooting.
Attorney General Jeff Sessions will attend instead of the president.
Senators Chuck Grassley and Lindsey Graham of the Senate Judiciary Committee detailed the information in a letter to new FBI Director Christopher Wray.
Senator Chuck Grassley, chairman of the Senate Judiciary Committee, has championed the accusation involving Andrew McCabe for months
The favorable recommendation was expected as more than half of committee members had publicly expressed support for Wray.
Since 1972, the average length of time between the nomination and confirmation of a director has been 20 days, excluding the special second appointment of Robert Mueller.
“My loyalty is to the Constitution and to the rule of law,” Wray told the committee.
Trump’s pick to succeed James Comey appeared for his confirmation hearing before the Senate Judiciary Committee.
The president's pick to replace James Comey represented an American client facing scrutiny from the Russian government.
Some ex-FBI agents said Wray must show he is not beholden to the Trump administration amid the “swirl of allegations” regarding Trump and Russia.