President Reagan telephoned to congratulate press secretary James Brady on his 41st birthday today and White House reporters here staged a special birthday show.

The president called Brady at his hospital room in Washington from the presidential ranch west of here at 11:30 a.m. Washington time and chatted for three minutes.

In a statement, the president said, "Jim Brady is a talented and dedicated public servant. He is my friend and I am proud to have him as my press secretary. Nancy and I salute 'the Bear' and Sarah today and we look forward to celebrating his next birthday in his office at the White House."

Several White House correspondents delivered greetings and good-humored insults to Brady over the telephone line to his hospital room. The show, organized by CBS correspondent Bill Plante, included group singing of "Happy Birthday" and "For He's a Jolly Good Fellow."

Associated Press radio correspondent Walter Rodgers delivered a startling imitation of the call of Brady's favorite bird, gavia immer, or the common loon.

UPI correspondent Dean Reynolds told Brady, a Chicago Cubs fan, his best wishes and commented that this season "for the first time the Cubs have a chance to finish last twice."

Brady's wife, Sarah, told the press and presidential staff at the Santa Barbara Sheraton after the show that Brady "has the biggest grin on his face he has ever had in his life."

Brady is recovering at George Washington University Hospital from a serious head wound suffered during the attempted assassination of President Reagan March 30.