Story highlights Four more protesters are arrested in Austin, Texas

Police arrest more than 24 people in Portland, Oregon, after warnings that a park is closed

Portland mayor: Authorities "worked really hard" to minimize confrontation

Scores of "Occupy" demonstrations continue across the country

The arrests occurred thousands of miles apart, but the scenes were similar in Oregon and Texas early Sunday: In the dark of night, police told Occupy demonstrators to leave protest sites. Those who refused were handcuffed and arrested.

Authorities in Portland, Oregon, and Austin, Texas, say protesters were trespassing and violating city rules. Demonstrators say authorities were infringing on protesters' rights to assemble.

Police arrested more than two dozen people who refused to leave a park in northwest Portland, Oregon, after warnings that the park closed at midnight, police said.

Authorities in Portland "gave protesters numerous opportunities to simply walk away or choose to be arrested," Mayor Sam Adams told CNN affiliate KPTV.

"This tonight was, I think, an unnecessary confrontation that we worked really hard to minimize," he said.

Occupy Portland offered a different take.

"Six mounted police and approximately 65 police in riot gear pushed supporters to the sidewalks and conducted the arrests over a period of several hours," the group said in a statement.

A Twitter post from the group as police entered the park said, "This is what a police state looks like."

Police also arrested 38 people in Austin, Texas, who had set up a table with food and other items outside City Hall two days after the city issued rules saying food tables at the event must be put away between 10 p.m. and 6 a.m. When the group was asked to leave the area, the 38 refused and were arrested, police said.

"A number of individuals decided to try to prevent the police from taking the food table, so they formed a ring around it. That's when they (police) started pulling people out arresting them," Occupy Austin member Ronnie Garza told CNN affiliate YNN.

Group members questioned the legitimacy of the city's new guidelines, saying they were not passed by a City Council vote, YNN reported.

"These were arbitrary rules that came from City Hall which is what spurred people to resist in a non-violent way," Garza said.

Austin Police Chief Aft Acevedo told YNN police were doing their jobs.

"We steam clean the plaza for health and safety reasons three times a week. The Occupy Austin members have always been very cooperative," he said. "Tonight, it looks like a few people decided to exercise civil disobedience and have been arrested."

Austin police arrested four more people Sunday afternoon, according to officer Dennis Farris.

Of the 38 arrested earlier, he said they are in the process of being released. If they return to the protest, they will be given "every opportunity to leave," said Farris. "We're going to bend over backwards."

Demonstrators across the country are protesting corporate greed and corruption. Many say the nation's wealthiest 1% hold inordinate sway over the remaining 99% of the population.

Scores of protesters have been arrested nationwide during the weeks-long "Occupy" movement.

On Friday, police said 51 demonstrators in San Diego, California, were arrested for various charges, including encroachment, unlawful assembly, illegal lodging and/or some form of obstruction of officers.

Three others were arrested on similar charges in Tampa, Florida, according to a police statement.

In Atlanta, police arrested demonstrators at a downtown park overnight Tuesday. The arrests came after Mayor Kasim Reed said he sent ministers to the park "to see if we can find a way to resolve this amicably."

In Nashville, Tennessee, authorities arrested more than two dozen protesters overnight Saturday, after they again defied a curfew imposed by the state's governor.

Twenty-six people received citations for trespassing, while two others were cited for public intoxication, according to Tennessee public safety spokeswoman Dalya Qualls.

On Thursday, Oakland, California, Mayor Jean Quan apologized for authorities' confrontations with demonstrators, who were tear-gassed. The clashes led to the hospitalization of an Iraq war veteran.

Marine veteran Scott Olsen suffered a skull fracture Tuesday night after allegedly being struck by a tear gas canister in Oakland, according to witnesses.

Despite recent crackdowns against demonstrators nationwide, the loosely defined "Occupy" movement does not appear to be losing steam.

In New York, where the Occupy movement was born, protesters braved snow, sleet and rain during an unusually early snowstorm in the Northeast this weekend.

Activist Angela Davis addressed the crowd on Sunday, stressing the importance of taking time to build real community.

"I'm persuaded that this is the beginning of something really wonderful, really vast, really great. And I should say that it connects with movements that are happening in other parts of the world," she told CNN's Don Lemon.