In his post, Peltz Beckham said he and his wife had travelled to London for Sir David’s birthday but were “rejected for a week as we waited in our hotel room trying to plan quality time with him”.
The pair were absent from Sir David’s 50th birthday party in May and did not post birthday messages online, reigniting rumours of a feud.
“He refused all of our attempts, unless it was at his big birthday party with a hundred guests and cameras at every corner,” the influencer wrote.
He said his father “finally agreed” to meet him but on the condition that his wife was not present, which he called a “slap in the face”, adding that his family then refused to see him on a subsequent trip to Los Angeles.
The eldest son said his younger brothers had been “sent to attack me on social media, before they ultimately blocked me out of nowhere this last summer”.
Cruz Beckham, 20, said in December that their parents would “never unfollow their son,” in response to a Daily Mail story claiming they had done so.
“Not true. My mum and dad would never unfollow their son. Let’s get the facts right,” he wrote on Instagram.
“They woke up blocked as I did.”
Ex-England football captain Sir David and former Spice Girl Lady Beckham have two other sons and a daughter – Romeo, 23, Cruz, and Harper Seven, 14.