The First Minister has said he is deeply concerned by the death of 24-year-old Mohamud Mohammed Hassan, as hundreds joined in a protest headed for Cardiff Bay Police Station.
He had been arrested on Friday at his home on suspicion of breach of the peace. He was later released without charge.
Mr Hassan was found dead at the same property later on Saturday evening, with his family claiming he had been assaulted while in custody.
South Wales Police has said his death was "sudden and unexplained" and said there were no indications of misconduct issues and or excessive force used by its officers.
The protest began in Cardiff city centre before proceeding to Cardiff Bay Police Station.
Mr Hassan's aunt, Zainab Hassan, told ITV Wales that she wanted him to be remembered as "the happy, loving young man that he was."
At First Minister's Questions on Tuesday Adam Price, the leader of Plaid Cymru, called for Mark Drakeford to do everything in his power to help Mr Hassan's family find answers.
He said: "Mohamud Hassan was a fit and healthy 24-year-old. On Friday evening, he was arrested at a property in Cardiff where neighbours reportedly spoke of a significant commotion".
"Having been taken into custody at Cardiff Bay police station, Mr Hassan was released without charge on Saturday. Later that evening he tragically died.
"Witnesses were reportedly shocked by Mr Hassan's condition following his release, saying that his tracksuit was covered in blood and he had severe injuries and bruising.
"There can be no doubt that this is a deeply harrowing case and every effort should be made to seek the truth of what happened - why was Mohamud Hassan arrested, what happened during his arrest, did he have legal representation, was there any aftercare, why did this young man die?
"Whilst we should not prejudge the outcome of any inquiry, will you commit First Minister, to doing everything within your power to help the family find those answers and do you support their call for an independent investigation of this case?"
In response, the First Minister said he found the case "deeply concerning" and said the circumstances must be properly investigated.
"I understand that the police have already referred, as they would have to, this matter to the independent police investigation service", Mr Drakeford said.
"The first step in any inquiry will have to be to allow them to carry out their work. I absolutely expect that to be done rigorously, and with full and visible independence.
"I'm glad that the family have secured legal assistance to them in order to pursue their very understandable concerns.
"And if there are things the Welsh Government can do, then I will make sure that we attend properly to those, without prejudging in any way the outcome of the independent investigations and now need to follow."
The Independent Office for Police Conduct (IOPC) issued a statement on Tuesday evening, saying they will be conducting a "thorough and independent investigation".
Catrin Evans, IOPC Director for Wales, said: "Our investigation will focus on the interaction police had with Mr Hassan during his arrest, the journey in a police van to custody, and the period of time he spent at Cardiff Bay police station including whether relevant assessments were made prior to his release.
"We will be urgently examining the extensive relevant CCTV footage and body-worn video.
"Accounts will be gained from the officers involved, and we will be seeking to speak to a number of witnesses to the police attendance on Friday evening and to Mr Hassan’s movements on Saturday after leaving custody.
“I would like to reassure people that we will carry out a thorough and independent investigation into the contact police had with Mr Hassan.
"We will be keeping his family, South Wales Police, and the Coroner updated throughout the course of our investigation.
South Wales Police has urged against speculation, saying their early findings "indicate no misconduct issues and no excessive force", but had referred Mr Hassan's death to the Independent Office for Police Conduct (IOPC).