"If the circumstances are such that a female Dalai Lama is more useful, then automatically a female Dalai Lama will come," the Dalai Lama said told reporters ahead of a 10-day tour of Australia.
The Nobel Peace laureate is scheduled to speak in Sydney, Melbourne, Adelaide and Darwin.
Asked about the gender war reignited by Ms Gillard, the 77-year-old monk said the world is facing a "moral crisis" of inequality and suffering and needs leaders who can bring compassion to their post.
"In that respect, biologically, females have more potential. Females have more sensitivity about others'
well-being. In my own case, my father, very short temper. On a few occasions I also got some beatings. But my mother was so wonderfully compassionate," the Dalai Lama was quoted as saying by Australia's AAP news agency.
His comments come as an Australian opposition leader sparked a controversy by using "grossly sexist and offensive" words to describe Gillard's body at a party fundraiser menu.
Gillard demands the political scalp of Liberal candidate Mal Brough over the controversial menu.
Opposition leader Tony "Abbott's solution to this pattern of behaviour is not to show any leadership. I mean, he's effectively stood by Brough," Gillard had said.
Earlier this week, she had warned the Coalition's (a group of centre-right conservative parties) "men in blue ties" would marginalise women and treat abortion as a political plaything if Labor lost the September election. She accused Abbott of a pattern of misogynist behaviour.