British newspapers have accused "workshy Wills" and his wife Kate of being idle and overzealous in their attempts to control the media, saying they had carried out far fewer official engagements than his grandmother Queen Elizabeth or her 94-year-old husband Prince Philip.
In an interview to mark the queen's 90th Birthday on Thursday, William, 33, said he was aware of the criticism and was willing to take on more royal duties.
"When the queen decides that she's going to hand down more responsibilities, I'll be the first person to accept them," he said in the interview released on Wednesday.
William said he had his "fingers in many pies" combining royal duties - he has just returned from a tour to India and Bhutan with his wife which garnered huge amounts of media coverage - with his role as a father with a young family and his job as an air ambulance pilot.
He said he took all three of these roles very seriously, and the queen and his father, heir-to-the-throne Prince Charles were fully supportive.
"I think the royal family has to modernise and develop as it goes along and it has to stay relevant and that's the challenge for me is how do I make the royal family relevant in the next 20 years time," William said.
In another interview, William said the queen had been an exemplary role model for him and a strong female influence especially after he lost his mother Princess Diana in a 1997 Paris car crash when he was 15.
He cited how she had told him off as he played on quad bikes with his cousins at Balmoral, the royal family's home in Scotland.
"I remember my grandmother being the first person out of Balmoral running across the lawn in her kilt and (she) came charging over and gave us the most almighty (telling off)," he said.