Saut Simatupang, the head of Indonesia's Vulcanological Survey, told Reuters that activity had reduced somewhat on Tuesday, but that the volcano remained a threat.
"Less smoke does not mean the volcano is safe," he said.
About 8,000 people have been moved from nearby villages, but there have been no reports of damage of casualties so far.
The evacuees are being housed in temporary shelters.
Halmahera is about 2,400 km northeast of Jakarta.
The last time ash and smoke streamed out of Gamkorna was in 1987, when no casualties were reported.
The last major eruption of the volcano is said to have taken place in 1673.
Indonesia is regularly hit by volcanic eruptions and earthquakes because of its location on the Pacific's so-called "Ring of Fire", a series of fault lines stretching around much of the Pacific Rim.