CANBERRA - Julia Gillard has made it a priority on her first full day in the top job

to resolve the damaging fight with the mining sector as she tries to regain voter support.

Ms Gillard on Friday spoke to world leaders, including US President Barack Obama, and held her first cabinet meeting a day after being installed as Labor leader and prime minister.

She met with Deputy Prime Minister Wayne Swan and Resources Minister Martin Ferguson first thing to begin working on a new strategy to resolve the impasse with miners over the proposed resource super profits tax (RSPT).

Having pulled a taxpayer-funded ad blitz selling the RSPT within hours of taking office, Ms Gillard has appealed to Australians to trust her to resolve the impasse which was a major factor in the demise of former prime minister Kevin Rudd.

"The decisions I have made this week have been decisions about profound matters of national interest. They have weighed heavily on me. They were not easy decisions," the prime minister said.

Ms Gillard maintained the Rudd government's line that she wanted to make sure Australians got a fair share of Australia's mineral wealth but was adamant the negotiations would be genuine and conducted in good faith.

"My priority obviously is to ensure that we deal with the question of the mining tax. It has caused uncertainty. I think that uncertainty has caused anxiety for Australians," she said.

With Labor having suffered a string of damaging polls, Ms Gillard has made it clear there will be further policy changes, including toughening up border protection in an effort to head off gains made by the opposition on the issue.

Opposition Leader Tony Abbott, who on Thursday said the change in leadership for Labor would make no difference to the outcome of the election later this year, now says he believes the coalition has a better chance of victory with Ms Gillard at the helm.

"I think what's happened is that Labor has exposed the underbelly, the ugly underbelly of factional power inside the Labor Party but they haven't changed the policies," he told ABC radio.

"So I think they are in fact in a weaker position now than they were just a few days ago."

Mr Abbott is looking to capitalise on gains made in the polls on the key issues of the mining tax, asylum seekers and problems with the school stimulus program.

There will be a cabinet reshuffle but it remains unclear whether Mr Rudd, touted as a possible foreign affairs minister, will be on Ms Gillard's front bench.

The prime minister said she had not personally spoken to Mr Rudd and no decisions had been made in terms of ministerial appointments.

Mr Rudd was not at the cabinet meeting.

Ms Gillard has promised to forge a different style as prime minister, vowing to be more inclusive in contrast to the centralised decision-making style of her predecessor.

"I trust ministers to get on with the job in their portfolio," she said, adding that she would work with them "side by side" on strategic questions.

"I believe that you get the best from people if you have them work as a team."

Before going into her first cabinet meeting, Ms Gillard spent the morning speaking to world leaders, including Mr Obama for about 20 minutes.

"The conversation was productive and very warm and reaffirmed the strength of our countries' longstanding alliance and partnership," Ms Gillard said.

Ms Gillard spoke to New Zealand Prime Minister John Key on Thursday afternoon and expressed regret at not being able to take Mr Rudd's place and address the New Zealand Parliament next week.

The prime minister was set to speak to other world leaders later on Friday including Indonesian President Susilo Bambang Yudhoyono, Malaysian Prime Minister Najib Razak, Canadian Prime Minister Stephen Harper and new British Prime Minister David Cameron.