Mr Wray gave evidence before the House Judiciary Committee as Democrats and Republicans clashed over the significance of Mr Trump's attacks on the agency.
The director's comments came days after Trump slammed the agency as a biased institution whose reputation is in "tatters" and "worst in history". Mueller is leading an investigation of possible Trump campaign links to Moscow.
"What I can tell you is that the Federal Bureau of Investigation that I see is tens of thousands of agents and analysts and staff working their tails off to keep Americans safe", Wray told members of the House Judiciary Committee when he was asked about Trump's remark.
Wray's testimony comes after the FBI has been the target of scornful attacks from President Donald Trump and some other Republicans who have alleged that special counsel Robert Mueller's investigation into possible links between Trump's campaign and Russian Federation during last year's presidential election is politically biased.
"Even the appearance of impropriety will devastate the FBI's reputation".
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Trump and his allies have "sought to undermine any institution that posed any challenge to him", said Tapper on CNN's "The Lead".
Wray's remarks in the House hearing were his first public response to Trump's tweet. His bosses, Attorney General Jeff Sessions and Rosenstein, remained publicly silent, leaving Wray to defend the agency.
Rep. Steve Chabot, R-Ohio, among others, specifically mentioned the fact that Strzok had a hand in adjusting former FBI Director James Comey's statement last summer about Hillary Clinton's email server.
Details from the charging documents related to former national security adviser Michael Flynn's plea deal and Trump's recent tweets have given fresh life to questions about obstruction of justice related to the president's decision to fire Comey, Wray's predecessor.
Mr Wray repeatedly deflected questions about the FBI's handling of the Clinton email investigation, saying the entire matter was under review by the justice department's inspector general.