Hugh L. Reilly, solicitor of the National Labor Relations Board, said last week that it was not improper for him to represent clients in a private lawsuit against a labor union last year while he was employed at the Labor Department.

"I'm totally comfortable with everything that I've done, and I don't think it does Congress any credit to equate my views with those of the Ku Klux Klan," Reilly said.

Rep. William L. Clay (D-Mo.) recently said Reilly was so biased against labor unions that appointing him solicitor of the NLRB was like putting a Klan member in charge of a black person's trial.

Until last week, Reilly had refused to defend himself publicly or comment on recent controversies at the agency, which referees collective bargaining disputes.

Board members came under criticism last month when the NLRB voted to give Reilly powers that the agency's independent general counsel traditionally has exercised.

Board Chairman Donald L. Dotson contended the move was necessary because the general counsel's staff had misrepresented the board's decisions in the past and because some staff members were "immature, . . . arrogant and overbearing."

But congressional Democrats said Dotson and other Republican board members were trying to circumvent the general counsel, who was appointed by President Carter and serves a statutory term.

The D.C. Bar entered the fracas last week when its 650 members who practice labor law said Dotson's characterization of the general counsel's staff was "unwarranted" and "not based upon . . . experience."

Dotson supporters, meanwhile, circulated copies of a 1980 newspaper article that quoted NLRB member Howard Jenkins Jr. complaining about misrepresentation. Dotson testified at a recent congressional hearing that Jenkins was a prime mover behind the board's power shift, but Jenkins said that he didn't think misrepresentation was a major problem.

Reilly said it was unfair for Congress to label him anti-union simply because he worked for eight years as a staff attorney for the legal arm of the National Right to Work Committee, a conservative group that opposes compulsory unionization.

"I'm for individual freedom . . . . If that means a person wants collective action . . . , I don't have any problem with that," he said.

Reilly also said no one at the Labor Department, including Secretary Raymond J. Donovan, objected to his participation in a case with which he had been involved before joining the department. At the time, Reilly was on Dotson's staff.

Last week a Donovan spokesman said Reilly withdrew from the case, which was financed by the Right to Work Foundation, after Donovan asked his staff to "look into the matter."

"The judgment of the department was there was no illegality, but that I might want to consider getting out of the case somewhere down the road," Reilly said. "No one told me to get out of it."

He withdrew two months after speaking to the Donovan aide, he said, but only because Dotson had asked him to become solicitor of the NLRB.