Malcolm Turnbull has been urged to provide "boring, competent, predictable government" while he settles into the prime minister role.
Mr Turnbull on Wednesday signed a deal with NSW and Victoria to fund the national disability insurance scheme and introduced laws on the China free trade deal and multinational tax avoidance.
He's also working on a new frontbench line-up, with new ministers set to be sworn in on Monday.
Liberal senator Arthur Sinodinos said regaining the trust of voters was a key job for Mr Turnbull in the wake of Tony Abbott's ousting.
He's expected to return to the ministry under the new leader he strongly backed.
"What we want is boring, competent predictable government," Senator Sinodinos told Sky News.
He expects Mr Turnbull will soon turn his attention to tax reform, including superannuation and the GST, to come up with a coherent package to take to the next election.
Mr Turnbull spent part of his first full working day in the top job talking to Senate crossbenchers and taking a phone call from US President Barack Obama congratulating him.
The White House said Mr Obama told Mr Turnbull he looked forward to working with him on "issues of mutual interest including regional security, the conclusion of the Trans-Pacific Partnership, and the continuing effort to address national security concerns such as the Islamic State in Iraq and the Levant".
The president also phoned Mr Abbott to thank him.
Independent senator Glenn Lazarus says he expects Mr Turnbull to be easier to work with than Mr Abbott, who had "no enthusiasm" to meet with crossbenchers.
Mr Turnbull won't be joining in the final days of the by-election campaign in the West Australian seat of Canning, which is being held on Saturday, but Labor leader Bill Shorten will hit the hustings.
Liberal candidate Andrew Hastie is expected to win the seat made vacant after the death of MP Don Randall.
Thursday is the last parliament sitting day until October 12.
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