Speaking at Number 10, he said “people need parks” but they must observe social distancing and not congregate in groups.
He also announced an extra £1.6bn for local councils in England.
And the ethnicity of victims will be recorded, in an attempt to understand why it affects some groups more.
Giving the government’s daily briefing, Mr Jenrick said he had “made it clear” to councils that all parks must remain open, after some closed their gates in recent weeks.
He said lockdown measures were harder for those without gardens or open spaces and that they needed to be accessible for “the health of the nation”.
Mr Jenrick said funerals can go ahead with close family members present so that they can say a “respectful goodbye” to those they love.
He pointed to the death of 13-year-old Ismail Mohamed Abdulwahab, from Brixton, who died after contracting Covid-19.
The tragedy was compounded after the family could not attend his funeral, he continued – adding: “That is not right and it shouldn’t have happened.”
Standing alongside the minister, NHS England’s medical director addressed the shortage of personal protective equipment (PPE) for NHS and other caring staff.
Prof Stephen Powis said it was “critical” PPE gets to NHS staff so they can follow the best possible guidance on its use.
Mr Jenrick said 400,000 gowns were arriving in the UK from Turkey on Sunday.
Councils are facing increased costs during the coronavirus outbreak, from supporting vulnerable people and providing essential services.
Mr Jenrick said council workers were the “unsung heroes” of the coronavirus response.
The additional £1.6bn announced doubles the amount the government has said it will pay.
Mr Jenrick has said the new total of £3.2bn in funding means an extra £300m would go to the devolved administrations – £155m for Scotland, £95m for Wales and £50m for Northern Ireland.
Local Government Association (LGA) chairman, Cllr James Jamieson, welcomed the extra cash pledge, saying it would give councils “breathing space”. But Richard Watts, the LGA’s resource chairman, had previously warned Mr Jenrick of “extreme cost-cutting”.
Mr Jenrick thanked 99-year-old Captain Tom Moore, who has raised an “astonishing” £23m for the NHS, and announced he would be guest of honour at opening of the new Nightingale Hospital in Harrogate next week.
He also acknowledged research was needed to better understand the disproportionate impact of the virus on people from BAME communities.
England’s chief medical officer has asked Public Health to look at what might be accounting for increased risks and increased deaths in particular groups.
Prof Powis said he was also concerned, especially as a number of NHS England staff were from the groups affected and he wanted to know what they could do to support and protect them.