Mexican officials have condemned US plans for a 700-mile (1,125km) fence along the two states' border, signed into law by President Bush on Thursday.
Mexican President-elect Felipe Calderon said the fence was "a grave mistake" which would lead to more Mexican deaths on the border.
George W Bush said the new barrier was needed to curtail illegal immigration.
Correspondents say the Republican party hopes the move will secure votes in next month's mid-term elections.
About 11 million Mexicans are thought to live in the US, more than six million of them illegally.
An estimated 1.2 million illegal immigrants were arrested last year trying to cross into the US via the border states of Texas, New Mexico, Arizona and California.
Mr Calderon said he deplored the move because "the fence doesn't resolve anything".
"Humanity committed a grave mistake in building the Berlin Wall," he said.
"I'm sure that the United States is committing a grave mistake in building this fence." Outgoing Mexican President Vicente Fox called the plans "shameful".
Mexico has pledged to challenge the fence at the United Nations, having already appealed to the Organisation of American States.
'Nation of immigrants'
In signing the Secure Fence Act 2006 into law, Mr Bush said his government would tackle illegal immigration by means of increased funding and numbers of immigration officials.
More than a million illegals were arrested on the border last year
He said that remote cameras, satellites and unmanned aerial vehicles would also be used to create a "21st-century" border with Mexico.
"Ours is a nation of immigrants - we're also a nation of law," Mr Bush said.
"Unfortunately the United States has not been in complete control of its borders for decades. Therefore illegal immigration has been on the rise."
However, he promised to balance the border plans with a temporary guest-worker programme and moves to grant citizenship to some of the illegal immigrants already in the US.
Those moves are opposed by many within his own Republican party.
The BBC's Nick Miles in Washington says that many there query how effective the fence will be.
TJ Bonner, president of the National Border Patrol Council, a union representing patrol agents, told The Associated Press that it would not be enough on its own:
"A fence will slow people down by a minute or two, but if you don't have the agents to stop them it does no good. We're not talking about some impenetrable barrier."
The BBC's Duncan Kennedy in Mexico City says opposition to the fence has united Mexican politicians.
They accuse the US of hypocrisy for enjoying the benefits of cheap Mexican labour but not being prepared to offer Mexican people a chance to cross the border legally.