Ricky Tonacia, 34, and Jack Dennard, 26, were questioned by police after flouting a highly publicised danger zone up to 10 kilometres (six miles) from the volcano.
Mount Agung has been periodically spewing molten clouds of ash and smoke for months, forcing the evacuation of tens of thousands of people living nearby - and drawing some foreign thrill seekers eager to climb its peak.
Authorities were alerted to the men's expedition after a nearby military post observed torch light on the volcano around 3:00 am local time Thursday (2000 GMT Wednesday), authorities said.
The pair and two Balinese men who drove into the exclusion zone to pick them up were detained several hours later as they attempted to descend the mountain.
Indonesia's disaster mitigation agency has said that the volcano remains at its highest alert level. Source: AAP
"We took them to the Selat Police post for questioning," Captain Wayan Mustika from the Karangasem military post told AFP.
"They said the hotel where they were staying told them the volcano is safe.
"We released them at 11:25 am because there was no criminal offence," he added.
Mustika added that a Russian man was briefly taken into custody after he was caught trying to climb Agung last week.
The volcano's alert level remains at maximum, but the 10-kilometre radius danger zone was reduced to six kilometres by Indonesia's volcanology centre on Thursday afternoon.
"Mount Agung is still in the eruptive phase and could impact settlements," the centre said in a statement.
Agung rumbled to life in September, forcing the evacuation of 140,000 people living nearby.
Activity decreased in late October and many returned to their homes, but the volcano has again been belching towering columns of thick grey smoke and ash for the past six weeks.
A spike in activity in late November sparked travel chaos, forcing hundreds of flights to and from the tropical holiday island to be cancelled and severely impacting its tourist-dependent economy.
