At least 200 prison inmates and militants and 30 security forces have died since IS militants attacked the jail on Thursday in a bid to free their members, officials have said.
There was no mention by the SDF of the 850 children and minors - including an Australian teenager - caught in the crossfire when the SDF aided by US forces began to storm the prison on Monday.
The United Nations and international aid organisations had expressed fear over the fate of the minors living alongside the nearly 5000 prisoners in the overcrowded jail.
The children were detained during US-backed campaigns that finally drove IS from its last territorial enclave in Syria in 2019.
Save the Children said earlier this week it was extremely concerned for the safety of a 17-year-old Australian boy held in the prison.
Sina'a prison is the biggest facility where the SDF has kept thousands of detainees, among them Arab youths who defied forcible conscription and others arrested for staging protests against Kurdish-led rule.
The Pentagon has confirmed that the US-led coalition carried out air strikes and deployed ground troops in support of the SDF operation.
"Daesh remains an existential threat to the region and it must not be allowed to regenerate," said US Major General John Brennan Jr., commander of Combined Joint Task Force, Operation Inherent Resolve, using the Arab acronym for IS.
"We must thoroughly investigate the circumstances that allowed this (IS) attack to happen," he said in a tweet.
Brennan also said the troubles exposed flaws in the overcrowded prison system.
"The makeshift prisons throughout Syria are a breeding ground for Daesh's failed ideology."
US-based Human Rights Watch says the SDF holds about 12,000 men and boys suspected of IS affiliation, including 2000-4000 foreigners from almost 50 countries.
The inmates are held in teeming prisons where conditions are inhumane in many cases, according to Human Rights Watch and other rights groups.
The Kurdish-led militia denies these allegations.
The mass detentions in recent years have fuelled growing resentment among Arab tribal members who accuse the Kurdish forces of racial discrimination, a charge denied by the Kurdish-led forces that rule their areas.
The Kurdish-led forces also hold about 60,000 Syrian and foreign women and children who are family members of militant suspects in squalid camps across the areas they control.
The fighting has also driven more than 45,000 civilians, mostly women and children, out of their homes in areas near the prison.
