Health Minister Robin Swann said he hopes that after the pandemic there will be a memorial for people who died with Covid-19 in Northern Ireland.
It has been a year since the first case of coronavirus was recorded in Northern Ireland.
The death toll recorded by the Department of Health is 2,055, with three more deaths reported on Sunday.
Mr Swann said he wanted his colleagues on the Stormont executive to consider a proposal for a memorial.
He said conversations had been held within the Department of Health about remembering those who had lost their lives.
"It's how we do this in a respectful way but also acknowledging the sacrifice of loss and also, at the same time, the sacrifice of service from our health service families," he told BBC Radio Ulster's Sunday Sequence programme.
"From many across our voluntary and communities sector as well, who helped their communities at the time that they were at their most vulnerable.
"So it's something I'm very keen to put a proposal forward to my executive colleagues about how we do that."
Reflecting on the beginning of the pandemic, Mr Swann said the projected number of deaths in Northern Ireland "shook" ministers and they had to prepare for the "worst-case scenario".
He said there would be a period of reflection and inquiry but that for now the world remained "in the teeth" of the crisis.
The former Ulster Unionist Party leader said that when he was appointed health minister in January last year it was originally intended he would serve as health minister for a "few months until things settled down".
However, there was a "conscious decision to keep that continuity" when the pandemic started.
A total of 112,493 positive cases of coronavirus have been recorded in Northern Ireland, with 136 confirmed on Sunday.
Saturday marked exactly one year since Northern Ireland recorded its first case.
In the Republic of Ireland six more Covid-19 deaths were recorded on Sunday, taking the country's total to 4,319.
Another 612 people have tested positive in the country in the past day.
More than half a million people in Northern Ireland have had a first dose of a Covid-19 vaccine.
That is about 27% of the overall population and about 35% of the adult population.
On Sunday police said a gathering of about 250 people at an "organised fight" was a "clearly a breach" of the Covid-19 lockdown restrictions.
The incident happened at a disused yard near Benburb, County Tyrone.
Police in Belfast issued 11 fines and four prohibition notices after a house party on Melrose Street in the early hours of Sunday.
They found a number of people at the property, some of whom were hiding in locked rooms and underneath beds.
A community resolution notice was also issued to a boy.