In an open letter, the Archbishops of Canterbury and York called on people to join a daily "prayer for the nation".
On Tuesday, the prime minister said he was "deeply sorry for every life lost".
Boris Johnson said he took "full responsibility", adding: "We truly did everything we could."
Archbishop of Canterbury Justin Welby and Archbishop of York Stephen Cottrell said the 100,000 people who have died "isn't just an abstract figure".
"Each number is a person: someone we loved and someone who loved us," they wrote.
They called on people, regardless of whether they have faith or not, to join in a "prayer for the nation" at 18:00 GMT every day from 1 February.
The archbishops' letter also highlighted that poorer communities, minority ethnic communities and those with disabilities have been "disproportionately" affected by the pandemic and "cry out for the healing of these inequalities".
Mr Welby and Mr Cottrell acknowledged the challenges of lockdown measures, including isolation and mental health struggles, with many losing their livelihoods.
"Also, the necessary restrictions we live with have also prevented us from being alongside loved ones as they died, or even at their graveside. All grief profoundly affects us, but this pandemic grief is so hard," they said.
However, they urged people to follow government guidelines, saying: "We show our commitment, care and love for one another by ensuring we do everything we can to stop the virus spreading."
They also encouraged everyone to get the coronavirus vaccine "as soon as it is offered to you", saying they were grateful for the "hope" it provided.
On Tuesday, a further 1,631 coronavirus deaths were recorded, taking the total number of people who have died within 28 days of a positive test to 100,162.
In a press conference at Downing Street, Boris Johnson said it was "hard to compute the sorrow contained in this grim statistic".
The prime minister said he took "full responsibility" for the government's actions, but added that "we did everything we could" to minimise the loss of life and suffering from the virus.
Separate figures from the Office for National Statistics, which are based on death certificates, show there have been nearly 104,000 deaths since the pandemic began.
The UK is the fifth country to pass 100,000 deaths, coming after the US, Brazil, India and Mexico.
A further 20,089 coronavirus cases were recorded on Tuesday, continuing a downward trend in the number of UK cases seen in recent days. The number of people in hospital remains high, as do the UK's daily death figures.
Speaking alongside the prime minister, England's chief medical officer Prof Chris Whitty said the number of people dying "will come down relatively slowly over the next two weeks - and will probably remain flat for a while now".
But a scientist advising the government has warned the UK could face as many as 50,000 more coronavirus deaths.
Prof Calum Semple, who is a member of the Scientific Advisory Group for Emergencies, told the BBC's Newsnight: "It would really not surprise me if we're looking at another 40-50,000 deaths before this burns out.
"The deaths on the way up are likely to be mirrored by the number of deaths on the way down in this wave. Each one again is a tragedy and each one represents probably four or five people who survive but are damaged by Covid."
He said the UK had experienced some "bad luck" with the emergence of a new, more transmissible variant but had also suffered from "decades of underinvestment" in the NHS and "a public health authority that's been eroded" .
Labour leader Sir Keir Starmer said it was a "national tragedy" to have reached 100,000 deaths and accused the government of not having learnt lessons over the summer.
Elsewhere, bereavement support charities have written to the health secretary calling for more funding in the light of what they call "the terrible toll of 100,000 deaths".
The National Bereavement Alliance, which represents a range of charities, said many families had been unable to be with loved ones as they died and to gather to support one another.
In the letter, they called for £500m of funding allocated to mental health in England in the spending review to be used to support the bereaved.
Minister for Bereavement Nadine Dorries said the government had given more than £10.2m to charities since March to ensure services were available to those who need them.
Insanity: doing the same thing over and over again and expecting different results.