Braulio Guerra, who represents the state of Querétaro, said it was "easy to climb the wall, but there are many dangers for our people". "Human rights, principles and dignity are non-negotiable," he added.
Mr Trump signed an executive order in January to jump-start the building of the wall, which he said was "so badly needed".
Experts later warned its construction could threaten 111 endangered animal species and cause major environmental damage.
Mr Guerra said building the wall would be an "absurd and unnecessary waste".
Mr Trump has repeatedly asserted that Mexico will foot the bill for the wall. It led to a very public falling out with Mexico's president, Enrique Peña Nieto, who had vowed not to cough up.
Following a series of tweets by Mr Trump, Mr Peña Nieto cancelled a planned visit to Washington.
Nearly two-thirds of Americans oppose the wall's construction, and 70 per cent believe the US will end up paying for it.
Mr Trump has said the price would drop "way down" once he became involved in the planning process. According to a leaked Department of Homeland Security report, the barrier could cost as much as $21bn (£17bn) and take more than three years to construct.
Some 650 miles of fencing already in place has come at a cost of $7bn ($5.6bn) and Mr Trump's plans require extending the barrier into increasingly remote and mountainous regions, which raises the building costs significantly.
The proportion of Americans who oppose the wall has increased since election day, from 54 per cent to 62 per cent.
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