Mr Trump and First Lady Melania Trump revealed they had the virus late on Thursday, hours after it was revealed by US media that White House aide Hope Hicks had earlier tested positive.
In a telegram sent to the White House, Mr Putin expressed “sincere support in this difficult moment” and hoped for Mr and Ms Trump’s speedy recovery.
“I am certain that your inherent vitality, good spirits and optimism will help you cope with this dangerous virus,” Mr Putin said in the telegram, according to the Interfax news agency.
The bombshell news Mr Trump is now ill, just weeks before November’s election, immediately threw the race for the presidency into chaos.
Mr Trump has gone into isolation at the White House and even if asymptomatic will be stuck there for an extended period of time.
Other get well messages for Mr Trump poured in from foreign capitals across the world.
“My best wishes to President Trump and the First Lady. Hope they both have a speedy recovery from coronavirus,” tweeted UK prime minister Boris Johnson.
European Council president Charles Michel wished America's First Couple a speedy recovery, tweeting: “Covid-19 is a battle we all continue to fight. Everyday. No matter where we live."
But disappointed by Washington's leadership during the global health crisis, some messages were laced with stinging barbs.
“This demonstrates that the virus spares no one, including those who have shown scepticism. I wish him a swift recovery," said Gabriel Attal, spokesman for the French government.
Hu Xijin, editor-in-chief of China's state-controlled Global Times newspaper, tweeted: “President Trump and the first lady have paid the price for his gamble to play down the Covid-19.
“The news shows the severity of the US’s pandemic situation. It will impose a negative impact on the image of Trump and the US, and may also negatively affect his reelection.”
Additional reporting by Reuters
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