Bill Shorten has pleaded for space as the investigation into Emma Husar’s treatment of staff continues, declaring the western Sydney MP to be a “good person”.

Husar announced she would take personal leave on Tuesday night, saying the publication of the investigation into her behaviour and treatment of staff, first reported by Buzzfeed, led to “threatening messages including threats of violence”, which she has referred to police.

“I’m a single mum and my first priority is the safety and wellbeing of my children,” she said in the statement announcing her leave.

“The best thing for me and my family right now is for us to be out of the spotlight, so I can access support.”

Among the allegations, which are being investigated by barrister John Whelan who has been engaged by the NSW Labor party, are Husar’s staff faced bullying, harassment and verbal abuse, and were made to perform tasks outside of their usual duties, including picking up after her dog.

Shorten, who said he was not made aware of the investigation until last Wednesday, said he would wait until the investigation was complete before looking at what action to take.

“But let me go to the heart of where I think your question is going,” he said at a Caboolture press conference, where he was repeatedly pressed on the issue.

“First of all, I think that Emma Husar is a good person. I certainly think that she’s going through a very tough time. I also think that other people have a right to fair treatment in the workplace and respectful relationships.

“What Emma has done, is she is putting her family first with all of this attentions. She’s going to take a little bit of leave – that’s not unprecedented – and I think that’s the appropriate course of action.

“Having said that, I do think that people are entitled to respectful workplaces and respectful treatment. Clearly, there are complaints, and so there are protocols in place and there is an independent investigation.

“Emma has been through a pretty tough family law process. That doesn’t make her an unusual person. What is hard to see, is the personal distress dragged out publicly.”

Network Seven broadcast vision of one of Husar’s staff members picking up after her dog during a walk on Tuesday night. Shorten did not explain why the animal was at her electorate office, but said it was not just a pet.

“The reason why I did choose to explain a little bit about Emma Husar’s circumstances is that she’s a single parent – one of her kids is diagnosed with and living with autism,” he said.

“The animal is a part of her son’s therapy and treatment.

“I suspect there’s more to this whole situation, and if I can, perhaps, just indulge you with one point here – there’s been a lot of family law stuff dredged out and circulating, I’m finding out in the last day or so.

“I don’t know if any of you have ever been through a messy breakup, and this doesn’t excuse any waste of taxpayer money and doesn’t excuse anything else. But I do get the sense that there is more to this situation than meets the eye. That is why I actually think it’s respectful to all the complainants, to Emma Husar and her family, to let an independent investigation take place.”

Labor figures have by and large fallen behind Husar with support, with Anthony Albanese and Mike Kelly both publicly defending the Lindsay MP.

Government MPs have called on Husar to be sacked, if the investigation finds against her, with Simon Birmingham saying Shorten must show leadership on the issue.

“If any of the allegations are true, then Emma Husar has no place on Bill Shorten’s team,” Birmingham told ABC radio.

“He should go to Sydney and dismiss her as an MP, disendorse her as a candidate and ensure that he takes responsibility for a member of his team where the allegations are clear, that they have been doing the wrong thing with their taxpayer funded staff.”

The workplace minister, Craig Laundy, encouraged Husar’s staff to take any of their claims to the fair work ombudsman, telling Sky News he did not believe it was “appropriate” for parliamentarian staff to be performing domestic duties.