The UK's chief medical officer, Prof Chris Whitty, said all of the latest to die were patients in "at-risk" groups.
All patients NHS England gave details of had underlying health conditions and were over the age of 60.
The reported deaths were from around England including London, Birmingham and Leicester.
Prof Whitty said: "I understand this increase in the number of deaths linked to Covid-19 will be a cause for concern for many. The public should know every measure we are taking is seeking to save lives and protect the most vulnerable."
He gave his "sincere condolences" to the friends and families affected, adding "every single one of us has a role to play" in reducing the spread of the virus.
The 10 patients were being cared for by nine NHS trusts in England including Buckinghamshire, Sandwell & West Birmingham, Wolverhampton, Leicester, Barts in London, North Middlesex and Chester.