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.
When announcing his death via a 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.
'Hearts of the nation'
Mr Hancock said Capt Sir Tom had been "a symbol of people's resilience during an incredibly difficult year".
"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?'," he said.
"We should find a way to make sure 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."
There was a one-minute silence in the House of Commons in honour of Capt Sir Tom, and all victims of the pandemic, ahead of Prime Minister's Questions.
Prime Minister Boris Johnson announced there would be a national clap for Capt Sir Tom and "all those health workers for whom he raised money" at 18:00 GMT.
Asked by a newspaper journalist later if he supported calls for a statue of Captain Sir Tom, the prime minister said the idea was "an excellent one".
"We will be working with his family to see what they think is most appropriate," he added.
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, originally from Keighley in West Yorkshire, 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.
Marston Moretaine'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 was always put your best foot forward, lift your chin up and meet what comes," she said.
"He'll be with us in spirit urging us onwards."
A notice placed in the village by Marston Moreteyne School said the children had been "lucky enough to be living next door to their very own superhero".
"We have watched as Captain Tom, in his quiet dignity and compassion, showed us how to live out our values - to take positive action to help others in our time of need," the message said.
"We won't remember a caped crusader but a superhero who showed us how to spread kindness and compassion to a whole world of people."
Karl Clark, landlord of The Bell pub in the village, said: "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.
The village postmaster, Bill Chandi, said he had been "shellshocked" at the news of Capt Sir Tom's death and, having known him for more than 20 years, he counted him as "a dear friend, not just a customer".
He said the Post Office handled about a quarter of a million 100th birthday cards for Sir Tom last year, and had already received more than 100 cards addressed to the family on Wednesday.
Chief nurse at 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."
A Facebook group called "Clap for Captain Sir Tom this Thur 4th Feb 2021. 7pm" has more than 85,000 members.
A BBC News special, Captain Tom: We Salute You, presented by Michael Ball, is being broadcast tonight at 19:30 GMT on BBC One and will be available on the BBC iPlayer.
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