While speaking with ABC's Radio's PM program on Wednesday, Mr Turnbull dodged naming his predecessor Tony Abbott directly.
"I'm not going to comment on the gentleman you described, you've referred to," Mr Turnbull said.
The prime minister has done his best all week to avoid discussing Mr Abbott's public critique of his government.
When asked about leaked audio of Mr Abbott criticising this year's Budget at a Liberal Party branch meeting, the prime minister replied: "The budget was a great success, it is a great Liberal budget."
The prime minister refused to comment on whether he believed Mr Abbott was deliberately trying to undermine his leadership.
"I know you're interested in the gentleman you described, but I'm not," he said.
Mr Abbott was invited to address a branch meeting on Monday night in the electorate of Liberal MP Michael Sukkar, who as Assistant Treasurer played a significant role in the budget, and didn't hold back.
"One of the reasons why I'm speaking out is not because I think we've got to change the personnel but because I think we've got to just move the direction a little bit," Mr Abbott reportedly said.
The former PM has made a number of guest appearances and radio interviews in recent days in which he's been critical of the direction of the Turnbull Government.
At the start of the week he claimed the Liberal Party of NSW was "haemorrhaging members" and said the way candidates are preselected needed to be reformed.
