Texas Governor Rick Perry - who is seeking the Republican nomination for US president - has said he would consider sending American troops into Mexico to combat drug-related violence.
Mr Perry was speaking during a campaign appearance in New Hampshire.
"It may require our military in Mexico working in concert with them to kill these drug cartels and keep them off our border," he said.
Such a move would go far beyond current US involvement in Mexico's drugs war.
The suggestion is also likely to irritate Mexico's government over the sensitive issue, correspondents say.
Governor Perry gave no further details of what sort of possible military intervention he would consider.
"I don't know all the different scenarios that would be out there," he said.
"But I think it is very important for us to work with them to keep that country from failing".
After the speech, the White House said it would continue its "historic level of cooperation with Mexico" to protect people on both sides of the border.
The Obama administration currently provides substantial material support to Mexican security forces, as well as close intelligence cooperation.
The US has also deployed National Guard troops to boost border security, and uses pilotless drone aircraft to gather intelligence inside Mexico.
Any deployment of US military forces on Mexican territory would almost certainly be unacceptable to the Mexican authorities.
Mexico lost around half its territory to the US after a war in the 1840s, and has since been very protective of its sovereignty.
The Mexican constitution also places strict limits on foreign intervention.
Mexican President Felipe Calderon has been pressing the US to do more to reduce demand for drugs among its citizens and to reduce the flow of weapons from the US to the cartels.
Correspondents say Mr Perry's comments may be aimed at showing he is tough on border security and illegal immigration - issues on which he has been attacked by other contenders for the Republican nomination.