The memory of Captain Sir Tom Moore is to be marked "properly and appropriately", the government said.
The 100-year-old, who raised almost £33m for NHS charities by walking laps of his garden, died with coronavirus in Bedford Hospital on Tuesday.
Health secretary Matt Hancock said he had "touched the hearts of the nation and we should remember that".
Meanwhile, dozens of tributes have been left outside the veteran's home in Marston Moretaine in Bedfordshire.
Capt Sir Tom was admitted to hospital on Sunday.
When announcing his death in Tuesday's family statement, his daughters Hannah Ingram-Moore and Lucy Teixeira said they "shared laughter and tears" with their father in their final few hours together.
They said his final year of fundraising had been "nothing short of remarkable".
He tested positive for Covid-19 last week. His family said due to other medication he was receiving for pneumonia, he was unable to be vaccinated.
Speaking to the BBC, Mr Hancock said Capt Sir Tom had been "a symbol of people's resilience during what was an incredibly difficult year" and "on behalf of everybody in the NHS, I'm very grateful".
The Army veteran won the nation's hearts by walking 100 laps of his Bedfordshire garden last spring during the first coronavirus lockdown, raising money for NHS Charities Together.
The fundraising group said that "when the time is right" it will also "put together a suitable tribute... in honour of everything he did for the NHS and NHS charities".
Capt Sir Tom had initially set out to raise £1,000 by walking 82ft (25m)-loops of his garden.
The charity said the total amount would rise to £39m when Gift Aid was taken into account.
Mr Hancock said: "When the NHS was under pressure during the first lockdown - he didn't just sit at home, he asked the question 'what can I do to help?'.
"I think that we should find a way to make sure that we mark the memory of Captain Tom and thank him for the contribution he made to the NHS.
"I will ensure that we mark his contribution properly and appropriately at the right moment.
"I think everybody would welcome that... he touched the hearts of the nation and we should remember that."
On Tuesday night, landmarks including Blackpool Tower, Wembley Stadium and the London Eye were illuminated in Capt Sir Tom's honour.
A book of condolence is being opened at St Mary's Church in Marston Moretaine.
The parish's retired vicar the Reverend Gill Webb said she remembered him as a "lovely gentleman".
"He didn't have a stress-free life... but his attitude to life was always put your best food forward and lift your chin up and meet what comes," she said.
"And that's what he did, he literally put his best foot forward.
"He has been such a ray of light for us in such horrible, horrible days and he'll be with us in spirit urging us onwards to keep our heads up high."
Karl Clark, landlord of The Bell pub in the village, said he thought there should be a permanent memorial.
"He was just a brilliant fellow, you looked at him and you just had to smile. He just cheered you up. If you were having a really bad day he just made you feel that little bit better," he said.
"I think his legacy will live on in his foundation.
"There has to be something for him... he's a legend, he really is."
Chief nurse at the the Bedfordshire Hospitals NHS Trust, Liz Lees, said it had been their "immense privilege" to care for Capt Sir Tom.
"We share our deepest condolences and sympathies with his family and loved ones at this incredibly sad time," a statement read.
"We'd also like to say thank you, and pay tribute to [him] for the remarkable contribution he has made to the NHS."
Formula 1 champion Lewis Hamilton tweeted that he was "honoured to have had the opportunity to be able to tell him how in awe of him I was".
"Captain Sir Tom was a true hero and we will never forget the incredible man who brought out the best of us at such a difficult time," the seven-times world champion from Stevenage said.
Bedfordshire Police said the force was "deeply saddened" by his death.
"Thank you for bringing hope and unity to our nation during such a challenging time," it tweeted.
We are deeply saddened by the passing of Captain Sir Tom Moore and send our heartfelt condolences to his family. Thank you for bringing hope and unity to our nation during such a challenging time. Your incredible fundraising work will continue to inspire us. pic.twitter.com/KA7IkqiKZo— Bedfordshire Police (@bedspolice) February 2, 2021
Capt Sir Tom joined the Army at the beginning of World War Two, serving in India and Myanmar, then known as Burma.
He was originally from Keighley in West Yorkshire and was made an honorary colonel of the Army Foundation College in Harrogate on his 100th birthday.
Capt Sir Tom became the oldest person to have a UK number one single when he recorded You'll Never Walk Alone with Michael Ball last year.