Andris Berzins said many defenceless people had been killed in “our own made disaster”, and called for foreign experts to investigate what happened.
Fifty-four people have died since part of the roof collapsed on Thursday, and at least seven people remain missing.
Late on Saturday afternoon, the last remaining section of the roof caved in, causing panic in the surrounding area.
Officials have said soil and materials from a garden being built on the roof of the shop may have caused Thursday’s collapse.
Latvia has begun three days of national mourning for the deadliest disaster since the former Soviet republic gained independence in 1991.
“These three days of mourning are very necessary to go from the mindset of helplessness to rethinking what each of us has done so that we can act in practical manner, because this is an event where we must clearly say that this is a large scale murder of many defenceless people and act accordingly,” President Berzins told public LTV broadcaster.
He said an investigation should be held at “maximum speed”.
And he went on to say: “While not undermining the professionalism of our builders, I believe that we should call upon international expertise which is in no way connected with our construction business.
“We cannot call it a natural accident, because nature wasn’t involved. The evening was calm and silent with a little fog. This is our own made disaster.”
The BBC’s Damien McGuinness said it caused the neighbouring building from where he was reporting – a shopping centre – to shake violently.
People in the shopping centre at the time panicked and ran out into the street amid fears it too would collapse, he said.
There were no reports of any fatalities. Our correspondent says only the four walls of the supermarket remain standing.
The rescue service immediately suspended operations until Sunday morning, saying it wanted to consult engineers about the risk of further collapse.
Until that point, rescue teams had been working round the clock, digging in the wreckage of the single-storey concrete and glass building to see if anyone was still trapped inside.
They periodically turned off all their equipment and asked the families of missing people to phone their relatives so they could pinpoint the ring tones in the debris.
Ten families have told the police that they believe their loved ones could be under the rubble, our correspondent says.
But, 48 hours on, hopes of finding anyone else alive are fading, he adds. By Saturday evening the death toll had risen from 52 to 54.
Three firefighters and two Russians are confirmed to be among the dead.
Many people have been laying flowers and lighting candles at the site of the tragedy.
Thirteen firefighters were among some 40 wounded, and 29 people were in hospital as of Saturday morning, the fire and rescue service said.
The initial collapse happened just before 18:00 (16:00 GMT) on Thursday, when the Maxima store was busy with customers.
About 20 minutes later another part of the roof caved in, trapping rescue workers who were trying to reach survivors.
Witnesses said customers tried to run out after the first part of the roof collapsed but the supermarket’s electronic doors closed, trapping them inside.
A rooftop garden with children’s playground was being built on the top of the building. There is speculation it may have been unable to support the large amount of building materials and soil that was believed to be on the roof at the time.
Local media said the building, rented by the Maxima chain, had been awarded a national architecture prize when it was completed in 2011.
But the inquiry will now investigate whether building regulations were broken.