A Pew Hispanic Center study shows immigration began to slow five years ago and may have reversed by 2010.

Economic factors, increased border control, and lower Mexican birth rates were all cited as factors.

More than 12 million migrants entered the US from Mexico since 1970, more than half legally, the report says.

"Looking back over the entire span of US history, no country has ever seen as many of its people immigrate to this country as Mexico has in the past four decades," the report's authors note.

However, figures clearly show major changes to the long-term trend over the years 2005-2010.

A decade earlier, from 1995-2000, some 2.9 million Mexicans arrived in the US, with just 670,000 people leaving the country for Mexico - a net influx to the US of more than 2.2 million people.

Between 2005-2010, though, just 1.37 million arrived from Mexico - and 1.39 million left to cross the southern border.

"While it is not possible to say so with certainty, the trend lines within this latest five-year period suggest that return flow to Mexico probably exceeded the inflow from Mexico during the past year or two."

The downward trend includes a sharp reduction in the number of illegal Mexican migrants living in the US, the report says.

The numbers of unauthorised Mexicans living in the US fell from nearly seven million in 2007 to 6.1 million in 2011, according to estimates based on US census data.

During those years the numbers of legal Mexican migrants in the US rose slightly, increasing by 200,000 to 5.8 million.

The data tallies with previous figures released by the US government that showed the Obama administration deporting record numbers of illegal immigrants for three successive years from 2009.

According to data in the Pew report, a "significant minority" of the 1.3 million people - between 5% and 35% - who left the US for Mexico did not leave the country voluntarily.

The issue of immigration is a sensitive one in a presidential election year.

New immigration laws in several states, including Alabama and Arizona, have placed a heavy focus on efforts to crack down on illegal immigration by requiring individuals to present valid US documents.

Backers of the new laws say the requirement to present documents encourages people without the legal right to be in the US to leave the country of their own accord.

That process of attrition was referred to as "self-deportation" during this year's Republican primary season.

Arizona's law is being challenged in the US Supreme Court on Wednesday.

Presumptive Republican nominee Mitt Romney polls badly among Latino voters, while President Barack Obama generally retains broad support despite his stern deportation policy.