Mexican Secretary of Foreign Affairs Luis Videgaray said that paying for a wall that US President Donald Trump wants to build on the border was "totally unacceptable", the media reported.
This led to the cancellation of the first meeting between leaders of the two countries.
"There are issues that are (unacceptable) for dignity, which have nothing to do with exports or the economy, but with the heart and pride of the Mexicans," Luis Videgaray said at a press conference at the Mexican Embassy in Washington on Thursday.
"Just as we offer respect, we Mexicans must respect ourselves, our history and national symbols," he continued.
Videgaray appeared before the media along with Mexican Secretary of Economy Ildefonso Guajardo at the end of their two-day visit to Washington to prepare for a meeting – cancelled on Thursday – between Mexican President Enrique Pena Nieto and his US counterpart next week, Efe news reported.
Earlier on Thursday, Trump had tweeted that it would be better to skip the meeting if his Mexican counterpart continued to insist Mexico would not pay for the wall.
The foreign secretary said he hopes to resume "high-level meetings" with the US government in "the next few weeks" despite the cancellation of the presidents' meeting and the "disappointment" and "surprise" from Trump's announcement that he had signed an executive order on building the wall.
"We reiterate the indeclinable will of the government of Mexico to continue in close communication at the highest level with the government of the US. We are going to continue to negotiate and we are going to reach very good agreements," he said.
Trump argues that Mexico must pay for the wall, his election promise, while for Pena Nieto's government, it is a red line that he will not cross.
Videgaray reiterated on Thursday that his country will not pay for the wall "under any circumstances" and that there were "things (such as the wall) that cannot and will not be negotiable".
"We recognise that the US is a sovereign nation with full right to protect its borders as the people and the government decide. We do not agree that the wall is the best way to protect or create a good coexistence between neighbours, but they can defend their borders as they see fit," he said.
"But claiming that it is the people of Mexico who pay for the wall is to move from a sovereign action to something that is deeply unacceptable," the foreign secretary added.
Videgaray also said that with a tariff on imports of Mexican products, such as the 20 per cent tax suggested by the Trump administration on Thursday, the border wall would end up being paid for by US consumers.
"A tax on US imports of Mexican products is not the way to have Mexico pay for the wall, but it is the American consumer who would have to pay more for avocados, washing machines and televisions," the foreign secretary added.