MEXICO CITY (Reuters) - Mexican President Claudia Sheinbaum said on Tuesday she would send a letter to U.S. President-elect Donald Trump, urging dialogue and cooperation following his pledge of across-the-board tariffs of 25% on Mexico and Canada.

"To one tariff will come another and so on, until we put our common businesses at risk," Sheinbaum said during a regular press conference, warning that tariffs would cause inflation and job losses in both countries.

Sheinbaum added that she would send the letter later in the day.

Trump made the pledge on Monday evening, blaming Mexico for not doing more to halt the arrival of illicit drugs and undocumented migrants via the countries' shared border.

Tariffs could violate the United States-Mexico-Canada Agreement (USMCA), which the countries signed in 2020 when Trump was president.

The Mexican peso weakened some 1.3% in early trading on Tuesday.

Sheinbaum said her administration had always shown Mexico's willingness to help fight the fentanyl epidemic in the U.S. and that apprehensions of migrants at the border were down and that migrant caravans were no longer arriving at the shared border.

However, Sheinbaum noted that criminal groups in Mexico were still receiving guns from the U.S. She said the region's shared challenges required cooperation, dialogue and reciprocal understanding.

"We do not produce weapons, we do not consume the synthetic drugs. Unfortunately we have the people who are being killed by crime that is responding to the demand in your country," she said.