Labor frontbencher Tony Burke has avoided being forced to apologise to parliament over claims that Speaker Bronwyn Bishop is biased and misused her office.

Speaker Bronwyn Bishop has defused a damaging blow to free speech in parliament by not insisting that Labor frontbencher Tony Burke apologise over claims she is biased.

Mr Burke had accused Ms Bishop of running roughshod over the independence of her role by allowing her Parliament House suite to be used for a Liberal Party fundraising event.

Such use of the suite was unprecedented and was yet another demonstration of her partisanship and bias towards the government, he said.

Ms Bishop has thrown out 101 Labor MPs, but only one coalition member, for misbehaviour in question time since she took the chair after the September 2013 election.

Mr Burke also asked the parliament’s privileges committee to investigate whether the fundraising event was an “improper interference” with the operations of parliament.

But parliament heard on Tuesday the event was not unprecedented.

Former Labor Speaker Leo McLeay used the suite for an ALP fundraiser involving businessmen in 1993.

Leader of the House Christopher Pyne, moving a motion to force Mr Burke to deliver an apology, said the Labor frontbencher had “grievously” reflected on the Speaker.

“He was deliberately trying to cast an aspersion on the Speaker and that aspersion was based on a falsehood,” Mr Pyne said.

Mr Burke apologised for saying the fundraiser was unprecedented, but did not resile from other criticism alleging the Speaker’s bias.

The coalition had no right to force an MP to make a statement to parliament.

“North Korea probably does stuff like this,” he said.

After the motion was passed, Mr Burke told parliament he had dealt with the matter and had nothing to add.

“If the members of the coalition think they can silence a member of the Labor party – bring it on,” he said.

Ms Bishop, who has the power to suspend an MP from parliament for 24 hours, said she did not accept that Mr Burke had properly apologised, but wanted everyone to move on from the matter.

“I hope that this salutary motion would bring about more decorum in this place,” she said.

Her wish was that MPs put aside “some of the things that have transpired in recent times” so that the people of Australia could “indeed feel more proud of us”.

The privileges committee declined Mr Burke’s request for an inquiry, telling Labor that it required a reference from the Speaker.