Tennis-Serena Williams pulls out of Australian Open

* American gave birth to first child in September

* Seven-times winner unable to defend title (Adds quotes, details and background)

MELBOURNE, Jan 5 (Reuters) - Serena Williams reluctantly pulled out of this year's Australian Open on Friday, the American saying that while she is close to regaining full fitness after giving birth to her first child in September, she is not ready to defend her title.

The 36-year-old was eight weeks pregnant last year when the American triumphed for a seventh time at Melbourne Park to claim an Open-era record 23rd grand slam title and then took the rest of the year off before giving birth to a daughter.

She has played just once in public since, losing to French Open champion Jelena Ostapenko in Abu Dhabi last week, but was still hopeful of making a remarkable return at the Australian Open until she admitted defeat a week ahead of the event.

"My coach and team always said 'only go to tournaments when you are prepared to go all the way'. I can compete - but I don't want to just compete, I want to do far better than that and to do so, I will need a little more time," Williams said in a statement.

Williams is the latest big-name player to withdraw from the year's opening grand slam, which will be played from Jan. 15-28, with Britain's Andy Murray (hip) and Japan's Kei Nishikori (wrist) having already said they would not compete.

There is also uncertainty over whether former champions Novak Djokovic and Rafael Nadal, the latter of which arrived in Melbourne earlier on Friday, will be fit to take to the court. (Reporting by Nick Mulvenney and Frank Pingue; Editing by John O'Brien)