In addition, they will no longer support a challenge against out-of-province doctors being called as witnesses.
Smith was 19 when she choked to death in a Kitchener, Ont., prison five years ago as guards, who say they had been instructed not to intervene, stood watch outside her cell.
The New Brunswick teen was initially incarcerated as a young offender, but was later transferred to the federal system. In the year before her death, Smith was transferred 17 times between nine institutions across the country.
Canada's correctional service had been arguing that Dr. John Carlisle, who is presiding over the inquest, didn't have jurisdiction to examine how Smith was treated in prisons outside Ontario. The correctional service had also taken the position that the videos shouldn't be played before the coroner's jury.
On Friday evening, the Smith family received a statement from legal counsel for the Department of Justice saying Canada is "withdrawing its submissions regarding the scope of the inquest and the issuance of out-of-province summonses."
Julian Falconer, lawyer for the Smith family, said the move paves the way for parties at the inquest to request summonses for a series of prison managers from outside of Ontario to be grilled over their handling of Ashley Smith.
"This is a huge one for the Smith family and all those who support the search for the truth about Ashley's death," Julian Falconer said.
"It is perfectly clear that the stark videotaped evidence shamed the correctional service into doing the right thing. One wonders what it would take for those doctors who treated Ashley Smith to feel the same sense of shame and allow us to get on with the inquest."
Corrections Canada told to 'co-operate fully'
Candice Bergen, parliamentary secretary to Public Safety Minister Vic Toews, said earlier in the day that the government had instructed Corrections Canada to "co-operate fully with the coroner's inquest" into Smith's death.
"That was our instruction and that's what we expect them to do."
Government lawyers had fought to keep videos depicting the teenager's time in prison from being released.
The screening this week of one disturbing video that shows guards duct-taping Smith and drugging her against her will prompted Prime Minister Stephen Harper to criticize correctional authorities for "unacceptable" behaviour.
There are still hours of videos that remain unseen by the inquest, but Bergen offered no clues as to whether they will be released.
Ashley's mother, Coralee Smith, said in a statement that her family had made a "very hard decision" when they decided "the Canadian public must see what happened to our daughter, so that this can never be allowed to happen again."
"I think about Ashley every day," said Smith, who thanked the public for the support the family received following the initial release of the video of her daughter in custody.The New Brunswick teenager was first charged with a criminal offence in March 2002, when she was 14 years old. In the following year, she faced charges of causing a public disturbance, trespassing and assault, according to a report from the New Brunswick Office of the Ombudsman & Child and Youth Advocate.
She was first incarcerated at age 15 after she threw crab apples at a postal worker. She was convicted of multiple charges of breach of probation, common assault, trespassing and causing a disturbance.
Carlisle's inquest is the second attempt to investigate the teenager's death. The first inquest, led by Dr. Bonita Porter, was halted when the presiding coroner retired.
Smith, who had a history of self-harm while incarcerated, spent much of the last year of her life in segregation.
The current inquest is expected to start calling witnesses in January.