WASHINGTON (AP) _ Five million immigrants are living illegally in the United States, the federal government said Friday, providing the first official estimate of the hard-to-count population in four years.

Undocumented aliens account for just under 2 percent of the U.S. population, the Immigration and Naturalization Service said.

``If there is one idea that comes out of looking at these numbers it is, as we have said many, many times before, that over the past two decades or so the country has had insufficient resources and attention to the illegal immigration problem,'' said Bob Bach, the INS executive associate commissioner. ``And it has accumulated to where it is now a large and substantial issue.''

Bach pointed to major funding increases provided in recent years, which doubled the INS budget since 1993, from $1.5 billion to $3.1 billion.

With more manpower, equipment and programs, the INS is deporting more people, beefing up enforcement at the Southwest border and ensuring that fewer illegal immigrants obtain work, he said.

``We have no reason to believe the problem is getting worse,'' Bach said. ``In fact we have every reason to believe ... that we are making significant progress.''

Bach's view wasn't universally shared.

``It is a huge indictment of the ineffectiveness of our immigration service that there are so many illegal aliens in this country,'' said Dan Stein, executive director of the Federation for American Immigration Reform.

Stein, a longtime critic of the INS and the Clinton administration's immigration policies, accused the agency of focusing too little attention on enforcement beyond the Southwest border.

With the undocumented immigrant population growing by an estimated 275,000 people a year _ at a time when the INS is deporting fewer than 100,000 people this year _ Stein said: ``The way the INS is going, it's like emptying a bathtub with a teaspoon without turning off the faucet.''

The illegal-immigrant population is fairly close to what it was before passage of a sweeping 1986 immigration law that gave amnesty, in the form of citizenship, to nearly 3 million people who were here illegally. Prior to then, depending on who is doing the counting, anywhere from 4.8 million to 6 million people were here unlawfully.

``The point is that the illegal population now is larger than it was before the amnesty,'' said Mark Krikorian, executive director of the Center for Immigration Studies. ``The amnesty has been totally negated.''

The latest estimates, based largely on Census data, cover illegal immigrants who live here at least a year, not those who slip in for a few days or months and then return home. INS said its estimates, which could be off by as much as 400,000 people in either direction, err on the high side.

The agency concurrently announced Friday that it was revising upward its 1992 estimate by half a million people, to 3.9 million.

Fully 40 percent of the undocumented population lives in California, which together with Texas, New York, Florida, Illinois, New Jersey and Arizona accounts for 83 percent of the illegal immigrants.

Texas, which was home to the third-largest undocumented alien population the last time INS provided estimates, has moved into second place, with 700,000, followed by New York with 540,000.

INS said more than half of the total undocumented population is of Mexican origin. El Salvador, Guatemala, Canada and Haiti were the other major countries of origin.

Forty percent of undocumented immigrants overstayed their visas, the agency estimates. The rest entered without inspection, crossing the U.S.-Mexican border illegally or coming in at other land, sea or air points.