By: ABC15.com staff, wire reports

PHOENIX - Officers have made dozens of arrests at rallies in downtown Phoenix to protest Arizona's new immigration law.

Hundreds of people are demonstrating against the law, despite a federal judge's last-minute decision to block the most controversial parts of the measure.

Watch LIVE video of the protests

Three people were arrested as the group rallied in front of the federal courthouse in Phoenix, and another woman was arrested later near the Maricopa County Sheriff's Office. Air15 video showed others being handcuffed too.

The area of 1st Avenue and Washington Street is congested and drivers are urged to avoid the area.

Also, protesters have rallied near the 4th Avenue Jail a few blocks away. There is a report that the jail is currently on lockdown. Air15 video shows protesters blocking the entrance to the sallyport where people are brought in for booking. Several are carrying signs and others are carrying flags. Sheriff's deputies are seen standing by, and have already arrested many.

Air15 video showed sheriff's deputies dragging protesters sitting at the entrance into the garage.

Deputies appeared to be urging other protesters and media to move away from the sallyport entrance. More deputies in riot gear formed a semi-circle around the garage entrance, but the crowd moved forward, appearing to force the deputies back into the garage.

Demonstrators first marched from the state Capitol at dawn on Thursday, then held a prayer service at a local church before heading to the courthouse where Judge Susan Bolton issued her ruling on Wednesday.

Chanting "Sheriff Joe, we are here, we will not live in fear," marchers then headed to the office of Maricopa County Sheriff Joe Arpaio, who has made a crackdown on illegal immigration one of his signature issues. Arpaio plans to send hundreds of officers into a neighborhood later Thursday.

Among the crowd was a drummer wearing a papier-mache Sheriff Joe head and dressed in prison garb.

Arpaio told ABC15 that Phoenix police officers are handling the situation as he focuses on a crime suppression planned for today. He also said through his Twitter account, "Just got a report that protesters are now trying to block my downtown jail sallyport and are chaining themselves to the jail." He also said, “I am prepared to arrest if protesters obstruct our operations.”

ABC15’s Jodie Heisner said through her Twitter account, “As many as a dozen protesters arrested. Now reports they are blocking entrance to 4th Avenue Jail.”

Authorities say Valley Metro light rail service has been affected by the protest activity.

Valley Metro Communications Specialist Andrea Libey said the stations at Jefferson Street and 1st Avenue and Jefferson and 3rd streets are not servicing passengers. Those passengers are being told to walk to the Washington station and they will board a shuttle train that will take them eastbound.

Libey said Westbound passengers are being told to de-board at 12th Street and continue on the shuttle train to Central Avenue and Van Buren Street.

There is no word on how long the detour will be in place.

Hundreds of Southern Californians are also rolling to Arizona this afternoon in nearly a dozen chartered buses carrying immigrant-rights activists left Dodger Stadium in Los Angeles for the ride to Phoenix.

Protesters say the point they're trying to make is that SB1070 is only a part of the problem.

"SB1070 is not the only thing that we're working against here. It's a much deeper and more historically rooted environment of racism," Florida resident Anna Rodriguez said.

Protesters and activists also made their presence felt at midnight on Thursday, when the new law went into effect.

People in anti-SB1070 shirts lined Guadalupe streets as part of a passive resistance, claiming they have been victims of racial profiling for years. Protesters said they hoped to send a message to Sheriff Joe Arpaio, and admitted they expected run-ins with deputies over their show of dissent.

Around 12:30 a.m., dozens of people could be seen blocking Avenida del Yaqui, the main roadway in and out of Guadalupe. At least three Sheriff's deputies were at the scene trying to control traffic in the area after four city buses were forced to stop on the side of the road.

Peaceful demonstrations also continued through the night at the State Capitol, where more than 100 people took part in a candlelight vigil. Groups moved the vigil onto 17th Avenue directly in front of the Capitol, forcing a section of the roadway to be shut down.