The public should express its appreciation of Britain's military "more loudly and more proudly", Prime Minister David Cameron said.
Speaking ahead of Armed Forces Day, he said the country had a "social responsibility" to show its thanks.
Writing in the Sunday Telegraph, Mr Cameron also called for "an explosion of red, white and blue" to mark Saturday's events.
Celebrations will take place across the country, with a main event in Cardiff.
Mr Cameron said his recent trip to Afghanistan, his first as prime minister, had served as a reminder of the risks faced by troops.
The BBC has learned that a review commissioned by Mr Cameron is likely to suggest that GPs contact war veterans to assess whether they are suffering from mental health problems brought on by their military service.
Referring to a number of recent military heroes from the Afghan conflict, the prime minister said: "These people know all about duty - they've lived it. Now we as a country must do our duty by them.
"Over the past few years there's been an increasing appreciation of what our Armed Forces do. But still I believe that we should do more."
He also said the government was playing its part through policies such as doubling frontline troops' operational allowances, renewing the military covenant, improving health and housing services for families and better co-ordinating treatment for veterans suffering mental illness.
"But supporting our Armed Forces isn't just a government responsibility - it's a social responsibility," he said.
"In the First World War those at home didn't just sing 'keep the home fires burning', they practised it. In the Second World War, the military occupied a huge place in the national consciousness, partly because everyone knew someone in uniform.
"I believe as a country at war we should see the same appreciation today, with the military front and centre of our national life once again.
"There is huge respect for the Armed Forces community out there, and I want that expressed more loudly and more proudly. As someone once said, silent gratitude isn't much use to anyone - so next Saturday I hope we see an explosion of red, white and blue all over the country."
Mr Cameron apologised following the publication of the Bloody Sunday inquiry this week, for what he said were the "unjustified and unjustifiable" actions of British soldiers when 13 people on a civil rights march were killed in in Londonderry 1972.
"But those wrongs cannot be allowed to cloud the reputation of our Armed Forces and the pride they inspire," he said.
Meanwhile, the BBC's Politics Show has learned that the review into the mental health of former service personnel may also recommend placing specially-trained psychiatric nurses in every mental health trust in the country.
The ongoing review, conducted by the Conservative MP Andrew Murrison, is examining how best to protect the mental health of Britain's serving troops and veterans.