The Prince of Wales shared the message on his official Twitter account alongside an image of himself, Harry and Archie.
While many pointed out Meghan and Camilla were missing from the picture, others suggested Charles should pick up the phone and call his grandson.
One said: “Hopefully you’ll decide to pick up the phone and wish your grandson a happy birthday.”
Another said: “I know he can’t come to you, but being a future King of England, & vaccinated, I would think you could go to him for a visit.
Prince Charles urged to put aside feud and call Archie
“I hope you at least Skype your grandson.”
Someone else asked why the message was posted on Twitter since Archie does not use the social media site.
They said: “Does Archie read Twitter? If not why post here?
“It only counts if it’s on social media?”
It is unclear whether Charles may have privately called Archie for his birthday.
Express.co.uk has contacted Clarence House for comment.
Charles has not seen his grandson since Meghan and Harry left the UK last year and moved to California after stepping down from the Royal Family.
In March, Meghan and Harry sat down with US media mogul Oprah Winfrey and made several explosive claims about their time within the Firm.
Harry claimed Charles stopped taking his calls but said he hopes time would heal their relationship.
The Duke of Sussex told Oprah he feels “let down” by his father, who he accused of a lack of support despite having gone through similar experiences.
He added: “Of course, I will always love him, but there’s a lot of hurt that’s happened.
“And I will continue to make it one of my priorities to try and heal that relationship.”
Harry also claimed he was “cut off” financially in the first quarter of 2020.
Last month, Harry reunited with his family at the funeral of his grandfather Prince Philip,
After the funeral, the Duke of Sussex was seen walking back to Windsor Castle with his brother Prince William.
While at the castle, the brothers spoke together with Prince Charles.
The Prince of Wales, however, is not believed to have spoken alone with his youngest son before he travelled back to California.
Prince Charles hasn’t been the only senior royal to publicly wish Archie a happy birthday today.
The Royal Family Twitter account, which represents the Queen and all the working royals without their own social media pages, wrote earlier today: “Wishing Archie Mountbatten-Windsor a very happy 2nd birthday today.”
Similarly, Kate and Prince William’s Twitter account Kensington Royal wrote: “Wishing Archie a very happy 2nd birthday today.”
Source: EXPRESS CO UK