The group said it would halt "offensive military operations" for one month to allow humanitarian groups access to the region. It urged the Burmese military to do the same.
Burma, which has previously labelled ARSA as "terrorists", appeared to reject the overture.
"We have no policy to negotiate with terrorists," Zaw Htay, a senior government spokesman, tweeted yesterday.
It came as further evidence emerged that Burma is laying mines on the border. One man lost his foot and another went to hospital in Cox's Bazar with serious injuries after standing on landmines, Amnesty International said.
Kaiser, a 10-year-old boy at a camp on the banks of the Tombro Khal River, needed stitches in his forehead after being hit by shrapnel when another refugee stepped on a mine.
"Luckily I got just a spark from it," he said. "I didn't see what happened to the man."