EXPLAINING THAT he has been "feeling kind of beleaguered" and under a "lot of pressure lately," Rep. Jack Kemp (R-N.Y.) has apologized to everyone concerned for an attack he made last week on the Congressional Quarterly and one of its reporters on pulic television's MacNeil-Lehrer Report.

The incident occurred last Tuesday, with Kemp's verbal barrage aimed at the magazine and its economic writer, Dale Tate, who was appearing with him to discuss his Kemp-Roth bill and how it will fare in Congress.

Kemp challenged Tate's impartiality and that of her publication, which has a reputation of neutrality and is generally regarded as the publication of recored for legislation.

Kemp was interrupted on the air by commentator Robert MacNeil, who said, "In defense of Congressionel Quarterly, they're usually very neutral on thses things." Afterward, according to Kemp's own account and that of Tate, the show's other host, Jim Lehrer, lambasted Kemp off camera for his behavior.

Kemp told a reporter last Friday that Lehrer "let me know in no uncertain terms that it looked like I went after CQ."

Lehrer has decilned to discuss the attack or its aftermath, but Tate said in an interview that Lehrer "blew up at Kemp. He said, 'We invited you here and gave you 15 minutes to present your case and instead you go ahead and attack a journalist who did just what shw was asked. She didn't give her own opinion.'"

Kemp said he had apologized to Tate and both MacNeil and Lehrer before they all left the studio that night. The next day, Kemp also called Peter Harkness, deputy executive editor of CQ, to offer to "apologize publicly."

"I made a mistake," Kemp told The Washington Post. "I'm big enough to admit it . . . I'm not embarrassed to say it."

Kemp said that he had "overreacted."

He blamed his outburst on his feeling that Tate had become "subjective" in her analyses and said he then became "subjective" also.

But "certainly," he said, "the Congressional Quarterly can withstand the heat of emotionally -- passionately -- subjective debate with a congressman."

When Kemp called Harkness the followng day to apologize, he said "that CQ was a wonderful publication and he had treated Dale Tate shabbily," Harkness said.

"I have never had a call like that from a public official and I get a fair number of calls from members of Congress," Harkness said. "Kemp kept saying that he was completely wrong, that he felt very badly about the whole thing and didn't know why he did it -- it was an extraordinary call."

"Kemp said he was under a lot of pressure lately because his proposal has been getting so much flak, and people saying it won't pass. I think he used the word 'snapped' -- that he just snapped when he heard it said again.

"I was just flabbergasted by the whole conversation, and it was hard for me to get a word in edgewise.He just kept saying what a dreadful mistake he's made and how everyone makes mistakes."

Harkness said Kemp asked if he could make a formal apology in some way, but Harkness said it wasn't necessary.

Kemp also acknowledged in an interview Friday that he had been under a lot of pressure since an Associated Press story published last Monday mentioned Kemp in connectin with a story about lobbyist Paula Parkinson.

The story, by reporter Janet Satinar, said that Parkinson was a frequent visitor to Capitol Hill Club, "patronized frequently by Republican, some of whom said they saw her there on numerous occassions with . . . Rep. Jack Kemp (R-N.Y.) and a number of others. Kemp acknowledged meeting her there.'What is she saying about me?' He asked 'I really have no idea. Our relationship was very casual. It wasn't even a relationship."

Kemp told The Washington Post that he was aware there were names of congressmen connected with Parkinson "floating all over town."

Kemp said that he met Parkinson at the Capitol Hill Club in the company of two other people "at a reception," and when asked, said he had never been alone with her or taken her to dinner or out for a drink.