The dead included a baby of eight months and a two-year-old toddler. Their father, the Pope’s nephew Horacio Bergoglio, is in serious condition.
The family were travelling on a highway in the central province of Cordoba when their car hit a truck from behind.
The Pope’s nephew — the son of Alberto, the Pope’s late brother — was admitted to hospital with multiple injuries.
Vatican spokesman Federico Lombardi said “the pope was informed about the tragic accident. He is deeply pained.”
He added the pope asks “all who share in his grief to unite with him in prayer.”
The accident happened a day after the Pope publicly broached the prospect of his own death for the first time, giving himself “two or three years” but not ruling out retirement before then.
Talking to reporters on a flight back to the Vatican from South Korea, the 77-year-old was asked about his global popularity, which was evident again during his five-day visit.
“I see it as the generosity of the people of God. I try to think of my sins, my mistakes, not to become proud,” he replied lightheartedly. “Because I know it will last only a short time.
“Two or three years and then I’ll be off to the Father’s House.”
The Argentinian-born Pope said he could handle the popularity “more naturally” these days — at first it had “scared me a little”.
While the Pope has not spoken publicly before about when he might meet his maker, a Vatican source said he had previously told those close to him that he thought he only had a few years left.
Pope Francis also mentioned the possibility of retiring from the papacy, as his predecessor Benedict XVI did last year, if he felt he could no longer adequately perform his duties.
Resigning from the papacy was a possibility “even if it does not appeal to some theologians”, he told reporters.
He added that 60 years ago it was practically unheard of for Catholic bishops to retire but nowadays it was common.
“Benedict XVI opened a door,” he said.
Francis admitted that he had “some nerve problems”, which required treatment. “Must treat them well, these nerves, give them mate (an Argentine stimulant tea) every day,” he joked. “One of these neuroses, is that I’m too much of a homebody,” he added, recalling that the last time he had taken a holiday outside of his native Argentina was “with the Jesuit community in 1975 ”.