The full-page advertisements placed in four New York newspapers today by Donald J. Trump calling for reinstatement of the death penalty grew out of the real-estate developer's ''deep-seated feeling that what's happening in society today has to be stopped,'' Mr. Trump said in a telephone interview Saturday.

The $85,000 worth of ads, in The New York Times, The Daily News, The New York Post and New York Newsday, refer to the attack by a gang of youths on a woman jogger and others in Central Park on April 19. The 600-word appeal, signed Donald J. Trump, is titled ''Bring Back the Death Penalty. Bring Back Our Police!'' The advertisement appears today on page A13 of The Times.

In the advertisement, Mr. Trump says that Mayor Edward I. Koch ''has stated that hate and rancor should be removed from our hearts.''

''I want to hate these muggers and murderers,'' Mr. Trump wrote. ''They should be forced to suffer and, when they kill, they should be executed for their crimes.''