Turnbull, who wrested the leadership from conservative Liberal Party colleague Tony Abbott in September, has threatened to hold national polls for both houses of parliament on July 2 unless the Senate passed two stalled bills relating to unions.
But the Senate this evening rejected for a second time legislation to reestablish a construction watchdog. It has already twice blocked a second industrial relations bill.
"The result of the decision in the Senate a short while ago... Means that the constitutional grounds for a double dissolution election exist," Attorney-General George Brandis said.
"It is not really an election campaign until the parliament is dissolved and the writs are issued, in my view," he told the Australian Broadcasting Corporation.
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Last month Turnbull recalled parliament to consider the bills and said if the Senate failed to pass them, he would set in train the process to dissolve both houses of parliament and issue writs for an election.
The government is set to deliver its annual budget on May 3, and Brandis said this would be a priority.
Turnbull's Liberal/National coalition government has been wavering in opinion polls, with a Newspoll published in The Australian today showing the opposition Labor Party ahead of the government 51 per cent to 49 per cent.
"As we move into the home stretch, you would expect the race to tighten because that is what always happens," he said.