He told TMZ on Thursday, "If she wants to be a royal, she needs to be a royal - she can't have it both ways.
"I think it's great for a US citizen or for a former movie star of Suits to be lobbying US senators.
"But when you lobby US senators, as Meghan Markle has done, as: 'I'm Meghan Markle, the Duchess of Sussex' - she's lobbying Congress and interfering from a position of using her royal title."
He pointed out that Meghan and her husband Prince Harry had decided to leave the royal family in 2020 and that the royals had a clear policy of neutrality when it comes to US politics.
"And her and Harry left the royal family. She did renounce her royal membership in the family."
Meghan's activism on the issue began last month, when she wrote to Nancy Pelosi and the leader of the Senate Chuck Schumer to ask for their support for the proposal.
She referred to her "modest background" growing up and said paid parental leave was vital for families like hers.
"I grew up on the $4.99 salad bar at Sizzler," Meghan wrote.
"I knew how hard my parents worked to afford this because even at five bucks, eating out was something special, and I felt lucky. I started working (at the local frozen yogurt shop) at the age of 13.
"I waited tables, babysat, and piecemealed jobs together to cover odds and ends."
She did not mention the $750,000 lottery win her father netted in 1990, which paid for her high school education at Immaculate Heart High School in Los Angeles.
Meghan also went to a private primary school, Hollywood's Little Red Schoolhouse nursery, from the age of 2.