A Mexican man has jumped off a bridge and killed himself just minutes after being deported from the United States.

Guadalupe Olivas Valencia, 44, on Wednesday threw himself to his death, authorities said.

With just a plastic bag of belongings in his hand, the Sinaloa state native jumped 30 metres from a bridge in view of the US border.

Witnesses said that the man was in great distress after being sent back to Mexico for a third time, according to the AFP news agency.

Soon after being inaugurated president on January 20, President Donald Trump ordered action to begin construction of a wall along the 3,145km US-Mexico border, a tightening of border security and tougher enforcement against undocumented immigrants inside the country.

His administration issued tough new orders on Tuesday to begin a sweeping crackdown on undocumented immigrants, putting nearly all of the country's 11 million undocumented foreigners in target for deportation.

Two memos signed by the Department of Homeland Security Secretary John Kelly make it easier for officials to automatically expel undocumented immigrants.

They order border patrol and immigration officers to deport as quickly as possible any undocumented immigrants they find, with only a few exceptions, principally children.

Kelly and US Secretary of State Rex Tillerson are due to meet Mexican President Enrique Pena Nieto and other high level officials in Mexico this week.