Trudeau was in Moncton, N.B., where he said the recent case of Tina Fontaine, a 15-year-old aboriginal girl found dead in Winnipeg, highlights the need to begin an inquiry.
"My heart goes out to the families of not just Tina Fontaine but of all the missing and murdered over the years," Trudeau said.
"The prime minister has shown himself not to be simply ... just out of touch with Canadians on this issue, but also on the wrong side of history."
Harper said earlier this week that Fontaine's death was a crime and should not be viewed as a "sociological phenomenon."
"There's no question that there's a criminal issue here, a horrible crime was committed," said Trudeau, who was campaigning with the provincial Liberals for the New Brunswick election.
"But it's part of a pattern that has gone on for years and Canada absolutely needs to get to the bottom of (it) with a national inquiry."
The federal Conservatives have said they prefer to address the issue in other ways such as through aboriginal justice programs and a national DNA missing person's index.
In May, the RCMP released a breakdown of 1,181 cases of aboriginal women who disappeared or were homicide victims. It said while aboriginal women make up 4.3 per cent of Canada's population, they account for 16 per cent of female homicides and 11.3 per cent of missing women.