Smith flew to Chile using a passport obtained in his birth name while on temporary release from prison on Thursday.
Chilean authorities have confirmed that Smith then took a flight to Brazil.
In Beijing for the Apec summit, Mr Key laughed yesterday as he told reporters he would alert Chilean President Michelle Bachelet about Smith when they met.
"I'll just let her know there's someone who could be out there from New Zealand that you may not want to invite round for lunch," he said.
Mr Key's joke raised eyebrows on Twitter, with Labour's corrections spokeswoman Jacinda Ardern among those to criticise the remark.
"Just heard the audio of John Key talking about Phillip Smith's escape ... and joking about it. Really Prime Minister?" she posted.
Zoe Walker added: "Did John Key seriously just get the giggles when talking about Phillip John Smith? WTF"
Herald columnist Tobey Manhire tweeted: "The greatest threat to PM Key has always been Comedy John. RT @hdpaNEWS: Phillip John Smith lols?"
By Matthew Backhouse of NZME. News Service
