Yesterday Mr Parker said he stood by the comparison.
"What I said wasn't a criticism of Mexico, it was a statement of fact. Mexico is a low wage economy relative to its neighbour, the United States, and despite the fact National promised the wage gap was going to close with Australia, it is now heading in the same direction [as Mexico]."
He said the size difference between the economies of Mexico and the United States was similar to that of New Zealand and Australia. Mexico's per capita GDP in 2010 was US$13,000 compared with the United States' US$42,000. New Zealand was US$25,600 compared to Australia's at US$36,500.
"It shouldn't be offensive for Mexican officials to have that statement of fact pointed out. We are in some ways in a similar position - we are neighbouring countries and Labour certainly doesn't want New Zealand to be a low-wage servicer of Australia."
In her letter Ms Rueda pointed out that this week Mexico was hosting the Economic Ministers Meeting in the lead-up to the G20 leaders' summit. Trade Minister Tim Groser is at that meeting - the first time New Zealand had been invited to attend.
She said there had been substantial investment in infrastructure and a growth in skilled work in industries such as aeronautics, telecommunications and biotechnology.
"Long gone are the days when the maquiladoras [assembly plants] were the only intensive job-creating resource!
"Honourable Mr Parker, I hope this information might be useful to you should you wish to make any other comments regarding the Mexican economy."
Mr Parker said he was keen on the suggestion of fellow Labour MP Phil Twyford who suggested Mr Parker be immediately dispatched to Mexico to deal with the "diplomatic crisis".
That was a tongue in cheek reference to Government minister Gerry Brownlee who was "invited" to Finland after he made comments about its crime rate and education system - causing a minor diplomatic row.