Mexican immigration to the United States, the largest wave of migrants from a single country in the nation’s history, has stopped increasing after four decades of surging growth and may be declining, according to a report released Monday by the Pew Hispanic Center.

In what the report called a “notable reversal of the historic pattern,” the number of Mexicans leaving rose sharply in the five years after 2005, while the new flow of migrants coming from Mexico into the United States fell steeply, Pew demographers found.

For the first time in at least two decades, the population of illegal immigrants from Mexico living in this country significantly decreased, according to the report. In 2011, about 6.1 million Mexicans were living here illegally, down from a peak of nearly 7 million in 2007, it said.

“We really haven’t seen anything like this in the last 30 or 40 years,” said Jeffrey Passel, the senior demographer at the Pew Hispanic Center and a co-writer of the report with D’Vera Cohn and Ana Gonzalez-Barrera. The center, a nonpartisan research organization in Washington that does not advocate policy positions, has provided some of the most reliable estimates for the elusive numbers of Mexican immigrants.