Immigration is a key issue in the run-up to the mid-terms elections

Mr Bush said the US had not been in control of the border for decades.

Illegal immigration is expected to be a major question in next month's US mid-term elections.

Mexican officials have opposed the fence, with outgoing President Vicente Fox calling it "shameful" and likening it to the Berlin Wall.

About 10 million Mexicans are thought to live in the US, some four 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.

'Nation of immigrants'

In signing the Secure Fence Act 2006 into law, Mr Bush said that his government would tackle illegal immigration by means of increased funding and numbers of immigration officials.

Ours is a nation of immigrants - we're also a nation of law

President Bush

Republican split Q&A: US immigration debate

He said that remote cameras, satellites and unmanned aerial vehicles would also be used to create a "21st-century" border with Mexico.

"We're modernising the southern border of the United States so we can assure the American people we are doing our job of securing our border," he said.

"Ours is a nation of immigrants. We're also a nation of law.

"Unfortunately the United States has not been in complete control of its borders for decades. Therefore illegal immigration has been on the rise."

But Mr Bush promised to balance the tightening of the border with a temporary guest worker programme and moves to grant eventual citizenship to some of the illegal immigrants already in the US.

Those moves are opposed by many within his own Republican party.

'Not impenetrable'

The BBC's Nick Miles in Washington says that, though few US congressmen have questioned the need for some action to reduce illegal migration, many have queried how effective the fence will be.

More than a million illegals were arrested on the border last year

TJ Bonner, president of the National Border Patrol Council, a union representing patrol agents, told 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," he said.

Mexico has pledged to challenge the fence at the United Nations and on Wednesday presented a declaration against the policy to the Organisation of American States, supported by 27 other Latin American and Caribbean nations but opposed by the US.

'Unnecessary and offensive'

The BBC's Duncan Kennedy in Mexico City says the fence has united Mexican politicians in opposition.

Across the political divide, politicians have come together to condemn what they see as an unnecessary and offensive barrier, he says.

And they accuse the United States 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, our correspondent said.

Part of the funding for the fence is likely to come from the $1.2bn (£0.6bn) set aside for it in a recent homeland security bill, but the full cost may be greater and the source of the funding is still unclear, our correspondent says.