The conservative government is giving priority to passing tax cuts that will cost AU$158 billion over a decade.
The government doesn't hold a majority in the Senate, so it will need either the support of the center-left opposition Labor Party or at least four of six unaligned senators to make the tax cuts law.
The opposition is divided on whether they should pass the cuts.
Treasurer Josh Frydenberg said the tax cuts were needed to stimulate a slowing economy.
"We are focusing on delivering these tax cuts for the Australian people as they endorsed at the most recent election," Frydenberg told Australian Broadcasting Corp.
"The Australian people spoke with a very clear voice just six weeks ago," he added.
The government was returned to office with a relatively narrow majority, holding 78 seats in the 151-seat House of Representatives where parties need a majority to form government.
Australia's central bank last month last month cut its benchmark interest rate by a quarter of a percentage point to a record low of 1.25% in the first rate change in almost three years.
The Reserve Bank of Australia on Tuesday reduced the rate further to 1%.