Malcolm Turnbull is under renewed pressure to call a banking royal commission after the Senate voted to establish a rare form of parliamentary inquiry into the banks.

The vote came as bank executives prepare to face a Senate hearing on Friday into the government's proposed $6.2 billion levy on the liabilities of five big banks.

A private bill co-sponsored by the Greens and crossbenchers - including One Nation, the Nick Xenophon Team, Derryn Hinch and Jacqui Lambie - to establish a commission of inquiry into banking and financial services passed the Senate with Labor support on Thursday.

The bill went to the lower house on Thursday afternoon, but did not progress to a debate despite the best efforts of the Greens and Labor.

Greens MP Adam Bandt told parliament other inquiries and reviews into misbehaviour and systemic problems in the banks had failed.

"If the government won't act, then the parliament will do the job for it," he said.

Opposition manager of business Tony Burke sought parliament's support to set a date for debate in August, hoping Liberal National Party MP George Christensen would back it.

With time running out on the final sitting day of the week, Mr Burke moved the motion be put.

Mr Christensen sided with government colleagues and, with the vote being tied at 70-all, Speaker Tony Smith cast his vote to defeat Labor and the crossbench.

Labor leader Bill Shorten said Mr Christensen was a "lion in Mackay and a mouse in Canberra".

"Today we saw the vaguely comical scenes of poor old Member for Dawson, bracketed by the treasurer, bracketed by the leader of the National party, in a witness protection program that will do the FBI proud," Mr Shorten said.

Mr Christensen said if Labor had moved to suspend standing orders, extend hours and bring on debate immediately on Thursday night he would have supported it.

"They almost had my vote," he told Sky News.

Another related bill to be moved by independent Bob Katter had his support, Mr Christensen said.

Government backbencher Warren Enstch, who has previously called for a royal commission, said the proposed commission of inquiry didn't address his concerns, describing it as political grandstanding.

He says he's been working with Treasurer Scott Morrison on a mechanism for resolving historical cases of bank misconduct worth more than $5 million.

It's understood up to six government backbenchers from rural electorates impacted by bank misconduct have been in discussions over recent months about potentially supporting the bill.

Nationals senator John "Wacka" Williams had vowed to cross the floor to support the bill in the upper house, but he wasn't required to since it passed without a formal division.

Greens senator Peter Whish-Wilson said it was a historic moment, with the Senate voting only for the second time since Federation to establish a parliamentary commission of inquiry.

The inquiry would hang over the prime minister and the banks "like a Damocles sword", he said.