In his first full day in office on Wednesday, Mr Turnbull indicated he wanted to have more women in his cabinet, which is due to be unveiled on the weekend and will be sworn in on Monday.
"If we are re-elected to the government, every single Australian will have a say".
Mr Turnbull has promised "a new style of leadership", citing Menzies, "small-L liberalism" and instilling greater weight in traditional Cabinet processes which have, perhaps, not been seen since John Howard's tenure.
"It's fair to say we've got a couple [of issues] we'll want to raise with him", Mr Key said.
The publication has allowed the Washington Blade to report its coverage of the Australian same-sex marriage debate.
Mr Hockey called a media conference on the introduction of multinational tax avoidance laws today, and refused to go into the details of his private conversations with Mr Turnbull.
As the new premier, Turnbull has indicated that Australia needs a stronger relationship with Israel.
According to the Australian constitution, the next federal election for the House of Representatives, the main legislative chamber of parliament, must be held by January 14, 2017 at the latest.
Executive Director of the Armenian National Committee of Australia, Vache Kahramanian, wrote to the Prime Minister-elect congratulating him on his election as Australia's 29th Prime Minister.
New Prime Minister Malcolm Turnbull has already gone some way to justifying his colleagues' decision to dump Tony Abbott, giving the Liberals a poll bounce. "It is a very legitimate and democratic way of dealing with it", he said, ABC reports.
Deputy Liberal leader Julie Bishop revealed on Tuesday night she knew Mr Turnbull was planning to challenge Mr Abbott "in the days beforehand".
Should Mr Morrison be promoted to Treasurer, his assistant minister and Turnbull ally Senator Mitch Fifield may be considered as his replacement.
Last, the one policy issue he addressed specifically in announcing his leadership challenge on Monday was getting the China-Australia free trade agreement over the line by the end of the year.