Prime Minister Justin Trudeau is giving no indication he is willing to intervene in the independent inquiry his government launched to examine the issue of missing and murdered Indigenous women and girls.

Trudeau faces a call from a coalition of frustrated families who suggest the time has come for him to restart the inquiry and rebuild it "from the ground up."

One of the inquiry's five commissioners quit this week, saying the process was unworkable.

The prime minister says the national public inquiry always faced a "tremendously difficult task", adding his government will engage with the commission to respond to the concerns of families who are seeking justice.

He also says Canada has dealt "inadequately" for decades with the ongoing national tragedy.

Trudeau's government has earmarked $53.8 million for the two-year study launched last summer.

Chief commissioner Marion Buller has indicated more time and funding will be required but she cannot say when a formal request will be made to Ottawa.