Malcolm Turnbull has used one of his first television interviews as Prime Minister to suggest the Today show co-host Lisa Wilkinson should be more "sunny" and "optimistic" in the morning.

Wilkinson, a veteran of the breakfast television slot who is all too familiar with a pre-dawn wake-up call, had dived straight into her first interview with the new Prime Minister on Monday morning, quizzing him about the dramatic shake-up in his cabinet after he seized the leadership from Tony Abbott last week.

Wilkinson highlighted the challenges Mr Turnbull faced, including the fact that 44 of his Liberal colleagues did not want him as leader.