Mr Kenny also claims there is a difference between statements being reported in the newspapers from Mr Halappanavar and his legal representatives’ statements.
In a disjointed performance in the Dail, he said the feelings of Mr Halappanavar were taken on board in removing members of the inquiry team from Galway University Hospital.
"It appears to me as if the legal team representatives of Praveen Halappanavar will not allow him to meet with the chairman of the investigation team," he said.
The chairman of the investigation team is not being allowed to speak to Mr Halappanavar because his legal representatives want a "full public sworn inquiry", Mr Kenny said.
"We need to find out the facts and the circumstances now," he said.
Mr Kenny said he wanted to "appeal directly to Praveen Halappanavar to meet with the chairman, Professor Sir Sabaratnam Arulkumaran.
Fianna Fail leader Micheal Martin called for an inquiry under the Commission of Investigation Act 2004, which allows for a speedy finding of the facts.
Mr Kenny said he had seen a solicitor's letter seeking a tribunal, which could be concluded within seven days.
The Taoiseach said it would be very helpful if the legal firm would say to Mr Halappanavar to sit down with the chairman.
He said there was no point in going down the long road of a tribunal.
Meanwhile, a coalition colleague has called for an independent inquiry entirely separate from the HSE.
Speaking in the Seanad, Senator O’Keeffe called on Dr Reilly to ask for the internal hospital report and to publish it.
“This report must have been started within hours of Savita’s death and should be complete by now – almost one month later,” she said.
“It would give a clear timeline and include all the facts from the paper trail which must be in place for any patient in any hospital.”