Ms Gillard was elected Prime Minister by her Labor Party colleagues when Kevin Rudd stood down at a morning caucus meeting.
Mining shares led a rally of the ASX200 in the early belief that Ms Gillard could scrap the contentious profits super tax.
She offered an olive branch to the mining industry, promising to scrap Labor's $A38 million ($NZ47.5 million) mining tax advertising campaign and saying the Government needed to do more than consult the resources sector to end the uncertainty caused by the profits super tax.
"We need to negotiate. That is why today I am throwing open the Government's door to the mining industry and I ask that in return the mining industry throws open its mind," she said.
However, once the reality of the tax remaining, in some form, sank in, mining shares retreated, Craigs Investment Partners broker Chris Timms said.
Treasurer Wayne Swan was promoted to deputy Prime Minister and was appointed by Ms Gillard to negotiate with the mining industry.
"Wayne Swan is the architect of this tax and he has been virulently opposed to any compromise, so it would be a big back-down for him personally. Gillard is from the left and was never a favourite of the mining industry," Mr Timms said.
The Australian dollar jumped briefly after the leadership changed, again on the speculation the Government would compromise on the mining tax proposal which had unsettled offshore investors.
RBC senior economist Su-Lin Ong said the elevation of Ms Gillard was positive for the Australian dollar and stocks in the short and medium term.
"It removes the political uncertainty that had been growing and would have only got worse. We assume Gillard will negotiate on the mining tax and produce a watered-down version. Longer term, we're not so sure it's good for bonds."
Ms Gillard was more left wing than Mr Rudd, favouring more regulation and spending and that meant the budget deficit would shrink more slowly than otherwise, Ms Ong said.
In the United States, stocks mostly fell in a volatile session after the Federal Reserve downgraded its assessment of the economic recovery as it vowed to keep cheap money flowing.
The Fed renewed its vow to hold benchmark interest rates exceptionally low, but its less bullish statement hurt a broad range of stocks. Banks were among the weakest.
Oil fell for a third day in response to the Fed statement.
