Enrique Pena Nieto says his country will not accept anything that goes 'against our dignity'.
Remarks contrast with Trump's description of Mexicans as "rapists" on the campaign trail.
"Mexico will pay for the wall," says president-elect, as he works to secure funding from Congress.
A harrowing video shows the Mexican twins crying while being held by a doctor in Chihuahua, Mexico.
Six people have died in clashes with the police and 1,500 people were detained for looting shops in the past week.
The Mexican government hiked the price of gasoline by 14 to 20 per cent on 1 January, sparking outrage among civilians throughout the country.
The icon, referred to as The Black Nazarene, is thought to have healing powers.
The post also took aim at the media, which Trump claims continues to treat him unfairly.
The victim has been identified as 31-year-old Christopher Ashcraft.
A $20,000 reward has been offered for information leading to the shooter's identification.
This comes just days after the US president-elect attacked General Motors for importing cars from Mexico.
Could the President-elect use a 2006 law to fund it via the government's annual spending package?
Ford said its new generation of electric cars will be built in the US following criticism from US President-elect Donald Trump.
Bloodshed continued along the once-popular beach tourist area.
Benny the elephant had lived at Ehecatl Ecological Park since 2014.
Thousands attended the party which hosted a race known as a 'chiva'.
35 people were killed and 70 others injured after a fire broke out at a fireworks market in Tultepec city.
The president-elect vowed to deport 'millions' of people during his election campaign.
The San Pablito market specialises in fireworks and has experienced disaster previously.
'In return for my husband's life, I will deliver your mother,' says a kidnap victim's wife in video.
The bill must also be passed by Mexico's lower house to become a law.
Now in custody, Joaquin 'El Chapo' Guzman faces extradition to US for drug and murder trials.