Many of the protesters who have made camp in Freedom Plaza in downtown Washington thought Monday would end with their arrests. By early evening, their organizers said they had been invited to stay.

The National Park Service, which grants permits for use of federal parkland, did not see it the same way.

The Park Service had met with organizers of the Stop the Machine group, which has camped since Thursday in the plaza just east of the White House.

But, said Park Service spokesman Bill Line, “nothing was agreed upon.”

Margaret Flowers said she understood that the group had been told it could stay for four more months.

Line said there were informal talks about the possibilities of extending the permit. “Nothing was finalized,” he said.

Permits have been granted for use of the plaza by other groups, he said. The parties to Monday’s meeting left with the understanding that efforts would be made to see what could be arranged.

Flowers said the group would take pains to accommodate other organizations that have plans to use the plaza in the coming weeks.

Many in the group expected a different outcome. Some thought that the permit expired late Sunday and that they would need to be gone by Monday afternoon. On Monday, Flowers said, Park Police officers told them their permit actually expired Monday night.

When expulsion was thought to be imminent, some said they were determined to stay or be arrested. Anne Wright had her attorney’s number written on her arm Monday.

“We’ll go out nonviolently kicking and screaming,” she said from a wicker chair.

“We bought one-way tickets,” said Don Anderson, a Vietnam War veteran who was camping at Freedom Plaza with a friend from Los Angeles. Anderson, who is paralyzed from the waist down and spoke from a wheelchair, said he will protest until he sees improvement in the government’s handling of veterans’ affairs.

The Stop the Machine group has made statements similar to the demands voiced by other groups — such as Occupy Wall Street and Occupy D.C. — that have set up in cities around the country. Protesters have expressed frustration with war, the economy and other issues.

Not far from Freedom Plaza, another protest has grown steadily in McPherson Square. In the 10 days since the Occupy D.C. group set up camp there, it has grown from a handful of protesters waving cardboard signs along K Street to a full-fledged encampment.

More than 100 people attend twice-daily general assembly meetings. Dozens have spent nights on air mattresses and in sleeping bags, then turned out for daily marches to the White House and elsewhere.

Group meetings and decision making also have taken root in Freedom Plaza. When the Park Police arrived Monday afternoon, they asked to speak with Flowers alone; she declined. She held a group meeting, whose members eventually agreed Flowers and another organizer, Kevin Zeese, could meet with police privately.

“They’ve been good to us so far,” Zeese said of the Park Police.

After the conversation with police, Flowers called another meeting. Members “were happy about” what they took to be the extended permit, Flowers said, though some insisted that, under the Constitution, “it was our right to to be here in the beginning.”

Occupy D.C. does not have a permit to occupy McPherson Square, but members say police have left them alone so far. “No one has any plans to ask for a permit — or to leave,” said Legba Carrefour, a self-described anarchist. “We haven’t had any problems with police.”

Staff writer Sylvia Carignan contributed to this report.