“Kimberley Kitching would want us to move on, to dedicate ourselves to a Labor victory at the election,” he told Today.
Mr Albanese said Senator Kitching’s death of a suspected heart attack at 52 was a “tragedy”.
But he rejected claims she had been bullied.
“The one issue that I’ve heard an inappropriate comment made to Kimberley Kitching was apologised for, and that was an appropriate action,” he said.
Prime Minister Scott Morrison has called Mr Albanese “gutless” over his refusal to call an inquiry.
Asked by Today host Karl Stefanovic if there was anything to that claim, Mr Albanese was scathing.
“This is a prime minister who went to Lismore and wouldn’t talk to any of the flood victims. This is a prime minister who had his security shut off streets so he doesn’t have to talk to people,” Mr Albanese said.
“This is a prime minister who won’t debate any issues in the Federal Parliament.
“This is a prime minister who refers things to the head of his department about what his office knew about issues related to Brittany Higgins, and we still haven’t heard what his own office knew.”
Speaking on Today shortly after Mr Albanese, Mr Morrison said his accusations were “complete rubbish”.
“When I went to Lismore, I did go and I spoke directly to those on dairy farms. I spoke to people in their homes. I went to their businesses,” he said.
“I just didn’t think it was good to put cameras in their faces because they were going through terrible trauma.
No, I didn’t go and talk to the green protestors, I didn’t go talk to those people.”
Stefanovic also pointed out to Mr Albanese that he had fought for several previous inquiries during the current term of government, asking why he was refusing to countenance one involving the Labor Party.
Mr Albanese instead framed the accusations of bullying by senior Labor figures as jostling over committee roles.
“There were no complaints (from Senator Kitching) put in any formal sense at all about issues,” he said.
“The one issue that was raised was Kimberley’s position on the Tactics Committee.
“From time the time on the Labor Party there’s a lot more people want to be in the Cabinet, in the outer ministry, in Assistant Minister roles, on the Tactics Committee.”
Mr Albanese said Senator Kitching had spoken to deputy leader Richard Marles about her suspension from the Tactics Committee, but that he was not party to what was said.
He said he had full confidence in Penny Wong as leader of the Senate, and that she and fellow Labor Senators Katy Gallagher and Kristina Keneally were “part of the solution”.
“In terms of moving forward, there was no complaint put in by Kimberley. My office is open to every member of the caucus,” Mr Albanese said.
“I had a number of one-on-one meetings with Kimberley since I’ve been leader and at no stage was any issues raised with me.”
Mr Albanese has proposed establishing a Kimberley Kitching award for human rights to pay tribute to her work.