Senator Kitching died suddenly earlier this month from a suspected heart attack at the age of 52.
In the wake of her death, reports have emerged the senator was ostracised and bullied by members of Labor's senate leadership team.
Politicians from both sides of parliament will attend Senator Kitching's funeral at Melbourne's St Patrick's Cathedral on Monday afternoon.
Prime Minister Scott Morrison said his thoughts were with Senator Kitching's family, but indicated Opposition Leader Anthony Albanese had questions to answers about the senator's treatment in parliament.
"The Labor Party and Anthony Albanese in particular has been very quick to throw stones, very quick to make accusations," he told Brisbane radio station 4BC.
"When (Anthony Albanese) has to deal with the same issues in his own house, well, he shuts up shop and gets into the basement."
Mr Morrison said the opposition leader had dismissed the claims about Senator Kitching's treatment, and that he had to address them.
"These are not things that have happened a long time ago, these are things that have just happened within weeks," he said.
"It is up to (Anthony Albanese) to address these things and take them seriously at the moment."
Labor frontbencher Mark Butler said Senator Kitching's funeral should be a day to celebrate her life and not to bring up divisive issues .
"Today of all days is not to go into a number of the claims being made and things being said over recent days," he told ABC Radio.
"Today is a day for the people who knew Kimberley to get around each other, hug each other and celebrate an extraordinary life that was ended far too early."
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