Two members of Republican Sinn Fein chaarged: Representatives of the group said Mr Dalton was detained as he made his way to a protest in Craigavon, over the condition of republican prisoners in Maghaberry.
A PSNI statement said police have arrested two men - aged 39 and 30 - in connection with an illegal parade through the Lurgan area in January.
Following news of Mr Dalton's arrest, Republican Sinn Féin supporters mounted a new protest outside the police station where he is being held in the Co Armagh town.
Josephine Hayden from RSF said the government has failed on promises to phase out strip-searching at jails.
"There was a march planned for tonight to highlight the condition of prisoners in Maghabbery and Des was coming to speak at that," Ms Hayden told UTV.
"The RUC pulled us in on Banbridge Street and arrested him because they said he attended an illegal march here in January. They need to leave him alone.
"There was an agreement to phase out strip searches, but they've completely and utterly reneged on that, absolutely and completely."
Ms Hayden said the arrest is not linked to violence that has erupted close to the police station on Wednesday evening.
It began with a security alert surrounding a suspicious vehicle at Lake Street, and has seen a number of cars burnt out and reports of shots being fired.
Two people, a 24-year-old man and a woman in her mid 20s, have been arrested for disorderly behaviour in connection with the destruction.
The area is now calm, however police are continuing their investigations and have appealed for any witnesses to come forward with information.
The Lisburn to Portadown rail line, which had been closed due to the trouble, is expected to re-open in the early hours of Thursday.
Upper Bann SDLP MLA Dolores Kelly has condemned those behind the violence.
"Someone's car has been stolen, positioned to block a key road and burnt out," she said.
"Meanwhile we have received reports that gun shots have been fired and major disruption has been caused to people due to traffic diversions and the closure of the train line.
"Their violent and destructive actions will get them nowhere. They will simply unite people in their rejection of these thugs."
Meanwhile in Belfast, an earlier security alert outside Strandtown Police Station in the east of the city has been declared a hoax.
Police were investigating claims to a local newsroom that a bomb had been abandoned in the area. The alert is now over and the Holywood Road has been re-opened.
Police have also carried out a number of searches in Newry, following reports that a suspicious object was left in the area. The police helicopter was tasked on Wednesday afternoon.
"To date, nothing suspicious was uncovered," a police spokeswoman said.
Police are urging people in the area to remain vigilant.