Mr Kahui's lawyer, Chris Wilkinson-Smith, objected to questioning by Coroner Garry Evans during the inquest at Auckland District Court today.
He said Mr Kahui was not given sufficient time to answer questions.
"He needs significant periods of time to form his answers. A series of questions, which don't fully allow him to answer each one, may diminish the value of his answers," Mr Wilkinson-Smith said.
Crown counsel Simon Mount said he thought Mr Kahui had been given ample time to answer all the questions put to him.
"The witness does not need protection from his lawyer before he answers questions in this court," Mr Mount said.
Marie Dyhrberg, representing Ms King, was concerned that Mr Wilkinson-Smith's constant interception of questioning could be sending a coded message to Mr Kahui on how to answer questions.
Earlier today, Mr Kahui said his then partner, Macsyna King, was "angry and hysterical" when she called him from the hospital where his three-month-old twin sons had been admitted with critical injuries.
He said he did not realise his twin sons, Chris and Cru, had life-threatening injuries until the police arrived at his door.
Mr Kahui has told the inquest he had never done anything to hurt his children.
He never hit them, hurt them or shook them in any way, he said.
Mr Kahui said he thought Ms King must have caused their fatal injuries.
"I have never done anything to hurt my children. I never asked Macsyna if she did it. I didn't do it so I thought she must have."
He denied he had ever used methamphetamine or cannabis, but admitted to occasionally drinking alcohol.
In the weeks leading up to the twins' deaths, Mr Kahui said he spent almost every day in hospital with his seriously ill mother, so Ms King looked after the twins most of the time.
He did not know she was using methamphetamine when the twins were at home, he said.
Cru and Chris died in hospital from severe head injuries in June 2006.
Mr Kahui was found not guilty of their murders in a High Court trial in 2008, at which his lawyers said Ms King killed them.
Ms King has denied she caused the injuries which led to the babies' deaths.
Mr Kahui will continue to give his version of events at the inquest today.
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