The Rocketman singer made the comments in a Twitter thread on Monday afternoon, hitting out at a "distorted and malicious account in the press" and the "relentless and untrue assassinations on their character".
The newlywed couple spent time at his south of France home after taking a private jet, which Sir Elton said he provided to provide the Royals with a "high level of much-needed protection".
The singer said he felt a "profound sense of obligation" to look after Prince Harry and his young family due to his close relationship with Princess Diana.
The singer added the couple have had a "hectic year" and showed "dedication to charity".
He said he "wanted the family to have a private holiday" in the "safety and tranquility" of his south of France home.
The couple have faced mounting criticism after reportedly taking four private jet journeys in 11 days, rather than opting for commercial flights, despite speaking out on environmental issues.
Buckingham Palace earlier declined to comment.
Dealing with the environmental concerns, Sir Elton John said he had made an "appropriate contribution" to a carbon footprint fund.
Finalising his Twitter thread, Sir Elton said: "I highly respect and applaud both Harry and Meghan’s commitment to charity and I’m calling on the press to cease these relentless and untrue assassinations on their character that are spuriously crafted on an almost daily basis."
The musician famously performed at the funeral of Harry's late mother Diana, Princess of Wales in 1997, singing a specially reworked version of his hit song Candle In The Wind.
He was also among the celebrity guests invited to Harry and Meghan's wedding in Windsor last year.
The Sussexes' trip to Nice to stay in Sir Elton's home followed a reported holiday to Ibiza to mark the duchess's 38th birthday earlier this month.
On Monday, Harry and Meghan posted a quote by Archbishop Desmond Tutu urging their followers to overwhelm the world with "little bits" of good.
It read: "Do your little bit of good where you are; it's those little bits of good put together that overwhelm the world."
The accompanying caption read: "An inspiring quote for the day - wishing you a wonderful week ahead!
"The Archbishop is an anti-apartheid and human rights activist, who was honoured with the Nobel Peace Prize for his continued efforts to champion equality for all."
But although the couple received many positive messages in response, some were critical, saying: "Doing your bit of good for the environment this week..." and "Stop flying private jets!!!!"
The duke has been vocal about environmental damage to the planet.
He said, in a quote on SussexRoyal last month: "Only now are we starting to notice and understand the damage that we've been causing.
"With nearly 7.7 billion people inhabiting this Earth, every choice, every footprint, every action makes a difference."
Harry met retired Archbishop Desmond Tutu on a trip to South Africa in 2015, when he presented him with the Order of the Companion of Honour, an award given to leading individuals for outstanding achievements in arts, culture and religion.
The duke and duchess and their baby son Archie are paying an official visit to South Africa in the autumn - their first royal tour as a family.