A Canadian truth and reconciliation commission wanted an apology from the Roman Catholic Church in its extensive list of recommendations in a 2015 report.
The report into a "cultural genocide" of more than a century of abuse collated evidence over six years from some 7000 former students in Canada.
Trudeau and the Argentinian pontiff had "cordial discussions" during their 36-minute private meeting, the Vatican said in a statement.
Without addressing the schools issue directly, it said the talks had "focused on the themes of integration and reconciliation, as well as religious freedom and current ethical issues".
Trudeau, a Catholic who was educated at a Jesuit school and a fervent backer of gay rights, later said that he told the pontiff "about how important it is for Canadians to move forward on a real reconciliation with the Indigenous people."
He added that he stressed to the pope "how he could help by issuing an apology".
Some 150,000 Indian, Inuit and Metis youngsters were forcibly enrolled into 139 residential schools, set up to assimilate native people and many operated by church groups on behalf of the Canadian government.
Many were physically and sexually abused and today blame their experience for a high incidence of poverty, alcoholism and domestic violence, as well as high suicide rates, in their communities.
Trudeau, having already offered his own apology to survivors, noted after the 2015 report that Pope Francis had previously offered similar apologies, for example over the treatment of Indigenous communities during the colonial era in South America.
The Canadian leader said Francis had reminded him that the pope's entire life "has been dedicated to supporting marginalised people in the world," and that he would work with Canadian bishops on finding a way forward.
Francis's predecessor pope Benedict XVI in 2009 expressed "sorrow" for the abuses in Canada. The first of the schools opened in 1874 and the last one closed in 1996.
Many survivors alleged abuse by headmasters and teachers, who stripped them of their culture and language.
At least 3200 students never returned home.
