The 82-year-old pontiff said he had been trapped in the lift for 25 minutes because of a power outage before he was freed by firefighters.
"I have to apologise for being late," a smiling Pope said at the start of the Angelus address.
He then asked the crowd for a round of applause for the firefighters.
Addressing the crowd, the Pope said there had been a "drop in voltage and the elevator stopped".
"Thank goodness, the firefighters arrived, and I thank them so much, and after 25 minutes of work they managed to get it started again," he said.
Television networks in Italy which broadcast the prayer live had been concerned the unprecedented delay might have been due to health reasons, AFP news agency reports.
In his address, the Pope announced that he would create ten new Roman Catholic cardinals next month.