With consular help Ms Puriri left the house, but could not take the children with her, he said.
She had been through several ups and downs since then.
"The good days are when Mohamed is calling making some promise and the bad days are when he doesn't respond at all.''
Last week, Ms Puriri had her visa extended and a senior representative from the Algerian Department of Foreign Affairs has contacted her to offer support, including legal assistance.
"I am still confident that Mohamed and Mihi will be able to reach and agreement that suits both of them and is in the best interests of the children and they'll be departing Algeria in the next week to 10 days.''
"Negotiations are continuing and we applaud Mohamed and Mihi for the efforts they are making.''
Yesterday is Zakaria's first birthday, but she had not been able to speak to him and was devastated to be marking the day alone, said the spokesman.
"She texted him four times yesterday and called and left two messages pleading with him to allow her to see Zakaria. No response, so she rang the family home and they hung up on her.
"She said she will be trying somehow to honour his birthday as best she can and celebrate his birthday as best she can in the environment she's in.'' he said.
There had been little food in the apartment while she was there, said the spokesman and Ms Puriri was also concerned about the emotional effects of the situation on the children.
"She's worried about the impact this is having on the children - whether the family are taking it out on the children and whether they're just being used as pawn in all this.''
Since leaving the apartment she has been taken to hospital in Algiers with frostbite in three toes because of freezing temperatures inside the Mostaganem apartment, and will have permanent nerve damage to two toes, said the spokesman.
Because the family planned to be in Algeria for only six weeks, they had not packed winter clothing, he said.