VENICE, JUNE 5 -- President Reagan warmed up for a taping of his weekly radio address today by relating an Italian-Irish joke, unaware that his remarks were being overheard.

At a recording session at the villa where he is staying before the economic summit, Reagan said he was going to tell "my gondola joke." The president's first few comments could not be overheard, but it appeared the story concerned a gondolier who was singing a popular Neapolitan song as he piloted his boat through the canals. The president sang the part of the gondolier as he told the rest of the joke:

"And the Lord said, 'I wonder what would happen if I took away 25 percent of his brainpower,' {as the gondolier was singing,} 'O sole mio'

"So the Lord did, {and the gondolier sang only part of the song:} " 'O sole, O sole.'

"The Lord said, 'Hey, I'll take half of it away,' {and the gondolier's song was shortened to} 'O so, O so.'

"Finally, the Lord said, 'What will happen if I take all of his brainpower away?' And he did. {And the gondolier suddenly switched his tune:} 'When Irish eyes are smiling.' "

As broadcast technicians laughed, Reagan said, "See, I can tell that, being Irish. I can't tell ethnic jokes except if they're Irish now." Reagan, an Irishman himself, laughingly added, "In fact, I can't go to Ireland anymore."