Roberto Suro, the director of the independent Pew Hispanic centre which released the report, told Associated Press: "The border has been the focus of federal efforts [to cut illegal entry] and has not produced a reduction in flow. Certainly that's an indication of ongoing demand."

The research was based on government figures for the number of people who had either entered the country illegally, overstayed visas, or violated immigration rules in some other way. The average figure for each of the four years up to March 2004 was 485,000.

If the rise has remained steady, the population of undocumented migrants would now be nearing 11 million.

Mexicans remain by far the largest group of undocumented migrants at 5.9 million, which is about 57% of the March 2004 estimate. Some 2.5 million others, or 24%, are from other Latin American countries.

Their presence, while illegal, has proved crucial to the American economy. Last week Wal-Mart, the country's largest employer, agreed to pay the government $11m (£6m) to settle accusations that it used hundreds of illegal immigrants to clean its stores.

Controlling immigration over the porous US-Mexico border will be a central topic when the Mexican president, Vicente Fox, meets George Bush in Texas tomorrow.

Latinos from South and Central America and the Caribbean are the largest ethnic minority in the US, having overtaken African-Americans in 2003, according to the US census bureau.