Updated

Homeland Security Secretary Janet Napolitano said Monday that U.S. communities on the border with Mexico are safer than most Americans believe, but also warned Mexican drug cartels they'll be "met by an overwhelming response" should they move north.

Napolitano told an audience at the University of Texas at El Paso — just across the Rio Grande from Ciudad Juarez and the unprecedented wave of drug-fueled violence engulfing it — that it's "inaccurate to state, as too many have, that the border is overrun with violence and out of control."

"This statement, often made only to score political points, is just plain wrong," said Napolitano, who was governor of Arizona before being confirmed as Homeland Security secretary in 2009.

Napolitano said violent crime has not spiked in U.S. communities across the roughly 2,000-mile border with Mexico. But the secretary also recognized that guarding against spillover from Mexican drug violence is an ongoing concern.

"Today I say to the cartels: Don't even think about bringing your violence and tactics across this border. You will be met by an overwhelming response," she said. "And we're going to continue to work with our partners in Mexico to dismantle and defeat you."

Napolitano said the Obama administration has increased the U.S. Border Patrol to more than 20,700 agents, more than double its size in 2004. She also said $600 million in funding signed last year by President Barack Obama will allow authorities to hire 1,000 additional Border Patrol agents and 250 new Customs and Border Protection agents to guard formal Mexico-U.S. border crossings.

An additional 250 Immigration and Customs Enforcement agents focused on transnational crime, as well as increased unmanned aircraft patrols, also are budgeted.

Texas Gov. Rick Perry often slams Washington for not sending enough manpower and money to secure the border state. He said last year that the $600 million was a good start, but not enough.

"The federal resources in Texas are woefully inadequate to secure the border with Mexico, and Gov. Perry will continue urging the Obama administration to do its job and protect our citizens from the ruthless drug cartels," Perry spokeswoman Katherine Cesinger said in a statement after Napolitano's speech. "It's unfortunate that a former border governor, who knows the implications of a porous border, continues to downplay the fact that there is a war waging within a stone's throw, or for that matter, firing range, from our border communities."

A sluggish U.S. economy has reduced the number of immigrants sneaking into U.S. territory and Napolitano said Border Patrol apprehensions declined 36 percent in the past two years as a result. But she also said U.S. authorities deported 779,000 illegal immigrants nationwide in fiscal years 2009 and 2010, more than ever before.

Last year, about 195,000 deportees were convicted criminals, Napolitano said.

"Let's stick with the facts and numbers when talking about where we are with the border," she said.

The statistics out of Juarez are nothing short of astounding. More than 6,000 people in the city have been killed by drug violence in the past two years alone, making it one of the most dangerous places on earth.

About 50 students protested outside the auditorium where Napolitano spoke, demanding justice for women slain in unsolved murders in Juarez, or for an end to the violence there. Others protested increased U.S. efforts to fortify its southern border at the expense of economic opportunity.

Napolitano said "a secure border does not mean a sealed border with no commerce."

During a 15-minute question-and-answer session with the audience, Napolitano said the U.S. had to do a better job stopping the flow of American guns smuggled south to fuel Mexico's drug war.

"I'm not here on a victory lap," she said. "We have more work to do."

Napolitano's address was part of a yearlong nationwide campus tour that began last week. She also was heading to Dallas on Monday to discuss Super Bowl-week security ahead of Sunday's contest between the Packers and Steelers at Cowboy Stadium in Arlington.