WA Premier Mark McGowan has previously accused his predecessor of being bitter, but now says he deserves respect from his Liberal colleagues as he weighs up his future in politics.
Opposition leader Mike Nahan last week urged Colin Barnett to quit after the former Liberal premier criticised his own second-term cabinet.
Speculation about Mr Barnett's future has been a distraction for the Liberal party since its election defeat in March, especially now when the opposition should be in a position to capitalise on the CV scandal of Labor MP Barry Urban.
Mr McGowan said on Tuesday that it was up to Mr Barnett to decide when to retire.
"I had my differences with him, I fought two very tough election campaigns against him," Mr McGowan told reporters.
"But he's served in parliament now for 26 years, he was the second-longest serving premier since the Second World War, I think he deserves some respect and I don't think his colleagues in the Liberal party are giving him the respect he deserves."
Mr Barnett has repeatedly said he will decide his future at the end of the year.
He has also indicated he may write his memoirs based on diary notes from his time as premier.
Asked whether would read the book, Mr McGowan quipped: "I'm sure I'll feature in it so I'll probably look up the index."
Senior Labor minister Alannah MacTiernan this week called for Mr Barnett to honour his achievements and allow his career to "die with dignity".
