Several thousand people have already moved away from Gunung Merapi, or Fiery Mountain, which has been rumbling and venting smoke for weeks, but officials put the total number of residents on and near the country's most active volcano at around 14,000.
Merapi killed 70 people in an eruption in 1994 and 1,300 in 1930.
Lava flows first seen spilling on Thursday from the side of the volcano, one of the most dangerous in the Pacific "Ring of Fire", were still visible, a state volcano observer said on Friday.
The latest spills were into a valley 200 metres from the mountain's peak, several miles away from inhabited areas on its slopes and in the foothills, said the Centre for Volcano Research and Technology Development in Yogyakarta.
A spokesman said: "It's still ongoing. Four trails of lava are flowing to the same place. However, the lava has not filled up the valley."
She said the conditions still did not compel authorities to raise the alert level to its highest notch, requiring the immediate evacuation of people living under the volcano, but Indonesian authorities have been urging people to leave voluntarily.
Lava seen flowing from Merapi
Yogyakarta, an ancient royal capital 440km east of Jakarta, is the nearest city to the volcano. The volcano is also close to Borobudur, a 1,200-year-old temple complex that attracts many tourists.