Commerce Secretary C. William Verity will leave for Tokyo today at a time when his department is pushing President Reagan to retaliate against Japan for refusing to give U.S. construction and engineering firms an equal shake in the bidding for major public works contracts.

While Verity said he is not going to negotiate the issue, the question of U.S. participation in $62 billion worth of Japanese public works projects remains the focal point of trade frictions between the two countries and is virtually certain to raised during the visit.

Verity, who will be the first Reagan administration Cabinet officer to visit Japan since Noboro Takeshita took over as prime minister 10 days ago, had lunch yesterday with Secretary of State George P. Shultz, who opposes retaliation against Japan over the issue.

The Commerce Department was backed at a sub-Cabinet level meeting Nov. 5 by other government agencies. The rest of the Cabinet is reported to back Commerce on the need for retaliation, and while Shultz opposes such action, administration sources said some senior State Department officials favor it

The immediate issue is the $8 billion Kansai International Airport near Osaka, which is now in the early stage of design and construction.

The possibility of the United States retaliating over Kansai was complicated by a letter former prime minister Yasuhiro Nakasone wrote President Reagan the day before he left office. The letter, addressed "Dear Ron" and signed "Yasu," urged the president not to retaliate against Japan over the construction issue.

Citing the "constructive working relationship" the two leaders maintained over the past five years, Nakasone said, "I believe the working principle for us has been that our two countries work jointly to resolve our problems rather than resorting to unilateral measures.

"It would be most unfortunate," Nakasone continued, "if the working relationship between the new Japanese administration and yours were to take off on the wrong foot. I earnestly hope you will be able to give a well-considered political decision on this issue from the viewpoint of the overall Japan-U.S. relations."

Administration officials, however, said that the Japanese negotiators have pulled back from commitments that Nakasone made when he met President Reagan in New York in September. Chief among them is the promise that any agreement on opening up Kansai and the $6 billion bridge over Tokyo Bay will apply to all future public works projects.

Administration negotiators privately say that all major contracts on those two projects have been allocated among the large Japanese construction firms, many of which are strong political and financial backers of Prime Minister Takeshita.