The Vatican opened the doors of the basilica shortly after 9am (1900 AEDT) on Monday. People then moved forward along the central aisle and past the body.
The Vatican's police and security force, the gendarmerie, estimated in the evening that about 65,000 people had come to the basilica on the first day.
Among the first mourners was Italian Prime Minister Giorgia Meloni. President Sergio Mattarella entered the basilica shortly before 9am, Agnello Stoia, the parish priest of St Peter's Basilica, told the ANSA news agency.
Benedict's long-time private secretary Georg Ganswein was also in the cathedral.
People had been lining up since the early hours of the morning, with a lengthy queue forming around St Peter's Square.
"I want to say goodbye to him," said one person from Germany who had started queuing during the night.
The funeral service is set to take place in St Peter's Square at 9.30am (2030 AEDT) on Thursday, followed by the burial in the basilica.
Pope Francis himself is set to say the funeral Mass. One Pope burying another is a historic event, made possible by Benedict's resignation in 2013.
According to official figures, up to 60,000 people are expected to attend the requiem, which Benedict had requested be kept simple.
The former pontiff whose birth name was Joseph Ratzinger died on Saturday morning in the Vatican at the age of 95. It emerged on Wednesday that his health had deteriorated.
German-born Benedict XVI was the head of the Catholic Church from 2005 to 2013, when, after just under eight years as pope, he voluntarily resigned, becoming the first Pope to do so in hundreds of years.
He cited his frailty, saying he lacked the strength for such a demanding job. His resignation may ultimately pave the way for future pontiffs to resign due to poor health.
Public viewing was set for 10 hours on Monday, and 12 hours each on Tuesday and Wednesday before Thursday morning's funeral at St Peter's Square.
In keeping with his wishes, Benedict's tomb will be in the crypt of the grotto under the basilica that was last used by St John Paul II, before the saint's body was moved upstairs into the main basilica ahead of his 2011 beatification, Vatican spokesman Matteo Bruni said.
Workers on Monday were setting up an altar in the square for the funeral Mass. Also being arranged were rows of chairs for the faithful who want to attend the funeral.
- with AP
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