PHOENIX (AP) - Thousands of people marched in the streets of Phoenix and Tucson on Tuesday to peacefully voice their frustrations over stepped-up immigration raids and what they see as unfair U.S. immigration policy.

As they walked 2 1/2 miles to the state Capitol in Phoenix in the nearly triple-digit heat, an estimated 15,000 to 20,000 people waved signs that read ``Stop the roundups'' and ``The sleeping giant woke up forever.''

March organizers, who previously thought between 5,000 and 10,000 people would show up, were pleasantly surprised when they saw Phoenix streets packed with demonstrators from sidewalk to sidewalk.

``If they had fear, they turned that fear into courage to come out and march,'' said Elias Bermudez, president of the activist group Inmigrantes Sin Fronteras, or Immigrants Without Borders.

Mayela Ruiz, an illegal immigrant, said she was afraid that marching might expose her to immigration authorities but that sending a message to lawmakers was too important to stay inside.

``I've been here 15 years. I've worked hard, paid my taxes. I've had no problems with the law and I'm afraid to leave my house,'' she said. ``I want a law that would allow me to work and live in freedom, but not like a slave.''

Jose Garduno, who came to Arizona illegally 20 years ago but has since gotten legal permanent residency, said he thinks every hardworking illegal immigrant deserves what he now has.

``When you don't have papers, everyone treats you differently,'' said Garduno, a loan officer for a mortgage company. ``When you've got your papers, you can fight for your rights. You don't have to hide from nobody. You have your own identity.''

Across the country, tens of thousands of protesters took to the streets from L.A. to Detroit. Chicago saw by far the largest turnout at about 150,000 people.

But Tuesday's marches fell far short of the million- plus protesters who turned out last year in demonstrations triggered by House Resolution 4437, also known as the Sensenbrenner bill. The bill, which passed the U.S. House in 2005 but was defeated in the Senate, would have made it a felony for illegal immigrants to live in the United States. About 100,000 people turned out for the largest demonstration in Phoenix last year.

This year's marchers were pushing for immigration reform that includes a path to U.S. citizenship for the estimated 11 to 12 million illegal immigrants living in the country.

Garduno said he thinks Congress will pass legislation sensitive to illegal immigrants. ``Last year, they heard us,'' he said. ``Before they didn't think we could do anything. But now they know we can.''

As thousands of immigrant-rights demonstrators arrived at the Capitol in Phoenix, several dozen counter-protesters with the Minuteman Project and other such groups confronted them.

The tension never escalated to violence, just strong words.

``I want to send them back,'' said Phoenix resident George Propheter, who held up a large handwritten sign that read ``Hell No.'' ``I've been in the city for 40 years. They've completely destroyed our city.''

Derrick Orozco, who works for a Mexican radio station, grimaced as a man walked by him and told him to ``Change your government,'' referring to Mexico.

``I think they're ignorant,'' Orozco said. ``They call it patriotism but it's racism. They crossed an ocean to get here. We just wanted to cross a dirt road.''

Phoenix police said they made no arrests.

Police in Tucson said up to 2,500 demonstrators marched to the federal courthouse and then to a park in the downtown area. One man was arrested and charged with disorderly conduct for throwing a water bottle at counter-demonstrators.