The initiative focused on border and customs staff, as well as combating the perception that Brazil was a place where anonymity was easily achieved.
Enhancing the country's ties with Interpol was part of the campaign.
The Brazilian newspaper Estado de Sao Paulo reported that during the 1990s, at least 60 western films featured a storyline where the criminal escaped to Brazil, or was seen holding plane tickets to the country.
Celebrity criminals such as 'Great Train Robber' Ronnie Biggs and high-publicity cases of former Nazi war criminals who evaded justice in Brazil have also played a part in heightening this perception.
Brazilian journalist Bruce Douglas told Newstalk ZB that Smith would easily keep a low profile in the country popular with fugitives.
His presence in the country wouldn't cause concern as Brazil remained one of the world's most violent countries, with a person murdered every 10 minutes.
Rio Times Online featured a CCTV image of Smith at Auckland Airport on its home page with the headline "New Zealand murderer Phillip John Smith escapes to Brazil."
One reader from Sao Paulo commented on the story: "I used to very highly respect New Zealand. Not so much any more. This is the type of criminal whose cell doors should be welded shut."