Malcolm Turnbull has been accused by the Federal Opposition of abandoning his beliefs to claim the prime ministership.

Labor used Question Time to accuse Mr Turnbull of compromising his views on same-sex marriage, renewable energy and climate policy.

"Has the Prime Minister sold out his principles to achieve his personal ambition?" Opposition Leader Bill Shorten asked.

"What other government policy is the Prime Minister willing to sell out to appease his personal ambition?"

Mr Turnbull has confirmed he will maintain the Coalition's position to hold a public vote on same-sex marriage after the next election.

He also said he would stick with the Government's direct action climate change plan and backed the Government's targets for global talks in Paris this year.

Mr Turnbull also declared he wants more women on his frontbench and expects his new ministry will be sworn in on Monday.

The Prime Minister has shifted responsibility for water from the Environment Ministry to Agriculture under a new Coalition agreement with the Nationals.

"The Leader of the Opposition consistently, and it's a problem shared by many people in his party, consistently confuses the means with the end," Mr Turnbull said.

"The object is to reduce emissions, we are reducing emissions.

"I support marriage equality. Many of my colleagues do not. Many of the Leader of the Opposition's colleagues do not.

"The question of how [to resolve the issue], that is the substantive issue. The question of how to resolve the matter, whether it is a free vote or a plebiscite, is a question of process.

"Each approach has its advantages."

Deputy Opposition Leader Tanya Plibersek also accused the Prime Minister of "mansplaining" in Parliament after he answered a question about foreign aid.

Mr Turnbull commits to more women on frontbench

In his media conference Wednesday morning Mr Turnbull would not be drawn into revealing any of the frontbench changes he is planning to make, but did confirm he wants more female representatives.

"There is no greater enthusiast than me for seeing more women in positions of power and influence in parliament, in ministries right across the country," he said.

"I can assure you that. I am very committed to that, but I am not going to say any more about the new ministerial arrangements.

"You don't have long to wait."

The ABC understands Immigration Minister Peter Dutton offered his resignation to Mr Turnbull in a text message on Monday night, but he also offered to stay and serve.

But Mr Dutton has refused to say whether he offered his resignation, and says he is waiting for Mr Turnbull to announce his ministry.

"I've enjoyed the Immigration portfolio very much, I'd be happy to continue in the portfolio," he said.

"But those ministerial arrangements are an issue for the Prime Minister and he'll make those announcements, as he's advised, at the end of the week."

Mr Turnbull said earlier Wednesday he had not spoken to Mr Dutton.

There has been much speculation about the future of Treasurer Joe Hockey, who was seen as the target of Mr Turnbull's economic criticism ahead of his move to overthrow former prime minister Tony Abbott.

The ABC's Barrie Cassidy said he had been told Social Services Minister Scott Morrison had been offered the position of treasurer.

According to his information, Mr Hockey was offered the chance to remain in Cabinet, and is likely to be offered the communications portfolio.

Mr Hockey called a media conference on the introduction of multinational tax avoidance laws Wednesday, and refused to go into the details of his private conversations with Mr Turnbull.

"I've had discussions with the Prime Minister," he said.

"We'll leave it at that. We'll see what happens."

Michaelia Cash is likely to be promoted to immigration and Arthur Sinodinos to employment.

Obama congratulates Turnbull, praises Abbott

US president Barack Obama has congratulated Mr Turnbull on becoming Prime Minister, as well as sending commiserations to Mr Abbott.

Mr Turnbull received a phone call from the White House.

A spokesman said the two confirmed the "shared values" between the two nations, and reiterated support for current cooperative arrangements.

Around the same time, Mr Obama phoned Mr Abbott, thanking the former prime minister for his work in tackling the Islamic State terrorist group.