Despite growing calls for an investigation – including by former Labor MPs – into claims Senator Kitching was bullied, the opposition leader said an independent was not needed.

“Kimberley Kitching would want us to move on, to dedicate ourselves to a Labor victory at the election,” he told the Nine Network on Wednesday.

“In terms of going forward, we have an ongoing review of all of our internal processes.”

Mr Albanese said Senator Kitching did not make a formal complaint about any bullying allegations and did not come to him directly with any concerns.

He said the late senator only raised an issue of being left out of Labor’s tactics committee with the party’s deputy leader Richard Marles.

“… There was no complaint put in by Kimberley, my office is open to every member of the caucus,” he said.

“We have processes in place now, if we can improve those processes, I’m certainly up for it.”

Albanese said there was always “argy bargy” from time to time within Labor, and the appointment and removal of MPs from various committees was a normal part of politics.

He hit back at comments from Prime Minister Scott Morrison that he was “gutless” for going to ground in the wake of the bullying allegations becoming public.

“I won’t be taking lectures from a prime minister who visited Lismore and had streets shut off so victims of floods could not get near him,” Mr Albanese said.

“I won’t be lectured by a prime minister who will not debate issues in parliament and who gags debate.”

As Labor’s national executive prepares to meet on Wednesday to find Senator Kitching’s replacement, former Labor MP Michael Danby said allegations she was bullied and ostracised by the party’s Senate leadership team should be independently examined.

“Australians expect (Labor) to be consistent with allegations of bullying,” he told Nine on Wednesday.

“They rightly were upset on behalf of Grace Tame and Brittany Higgins, and it’s one of our own sisters in our own camp who’s been badly treated in Canberra and treated worse in Victoria by some of the faceless men.”

Kitching was laid to rest this week following her sudden death aged 52, from a suspected heart attack in Melbourne on March 10.

The Senate will have a special sitting on Monday, at the request of the leaders of the government and opposition in consultation with other senators, to enable senators to speak on a condolence motion for Kitching.

The ALP national executive will also be asked to institute a Kimberley Kitching Human Rights Award, to be handed out at each national conference to a member who has demonstrated an “outstanding commitment to the advancement of human rights in Australia or globally”.