He did not name the "associate" who assisted him when renewing the passport last year.
Smith was dramatically arrested at a Rio de Janeiro hostel this week, after fleeing New Zealand while on a 72 hour "limited release" from Spring Hill Prison.
Smith's stepfather Basil said on Thursday he was worried his stepson would have a nervous breakdown in the Ary Franco jail, where he was first detained.
Dr Ellis said Smith had now been moved to a better prison, Bandeira Stampa, where had no specific concerns.
"Smith said his first prison, Ary Franco, was rough," Dr Ellis said.
"He said that Bandeira Stampa was a reasonable improvement in conditions, and that generally he was ok."
Dr Ellis said Smith had asked Brazilian prison authorities if he could to make phone calls from jail to contact a lawyer, but this request was declined.
The lawyer said he received notes with instructions from New Zealand embassy staff, who visited Smith in jail on Friday.
"Smith confirmed that he hadn't been in contact with any legal counsel since his arrest," Dr Ellis said. "The Embassy followed up with the Prison Deputy Director following the meeting with Smith, and he confirmed that no prisoners are allowed to make phone calls, even to make contact with legal counsel - all requests for legal counsel must be made by another party."
The escape was an embarrassment to Corrections and led to calls from the family of Smith's victims for Corrections staff responsible for Smith to resign.
Authorities here argued they could not stop the child molester and murderer fleeing New Zealand because his passport was in a name different to that he was incarcerated under.
Yet Traynor was the same surname Smith used when running a business from jail with convicted peeping tom David Edlin.
In this morning's statement, Smith named his parents as John Anthony Traynor and Patricia Elsie Traynor and described childhood trips overseas.
"I was never adopted but used the name Phillip John Smith from the age of four, Smith being my stepfather's name. In 1984/5 my passport under the name of Traynor was issued. It was used to travel to Fiji, New Caledonia, Tonga, USA, and Australia...
"My passport was renewed in 1987/88, and at age 13 or 14 I visited Australia. In 2013, I renewed it again, I completed the forms, and an unnamed associate posted them."
Next story: Smith set to return to NZ without a fight
