Authorities said the two new cracks were spotted in the Lanipuna Gardens neighbourhood, where residents were ordered to evacuate earlier this month after the volcano erupted and two major earthquakes rattled the island.
"This morning, activity is dominated by lava fountaining, explosion of spatter more than 100 feet (30.48 metres) into the air, and an advancing lava flow from fissure 17 at the northeast end of the fissure system," the Hawaiian Volcano Observatory said in a statement.
It added that lava was continuing to spew from multiple points of the active fissure system.
The latest cracks reported on Monday bring to 19 the number of fissures caused by the volcano eruption.
Fissure 17, which opened over the weekend, prompted more evacuations and warnings of a possible major eruption of the volcano.
So far, some 40 homes and other buildings have been destroyed by the red hot lava that has been flowing from the volcano.
Scientists have warned that as the lava level continues to drop in the crater, more fissures are likely to open in the ground and spew lava and toxic fumes.
Nearly 2,000 people have been evacuated from residential areas in the path of the lava flow and because of the toxic fumes.
Local authorities have warned that mass evacuations may be ordered as new fissures develop.
Kilauea is one of the world's most active volcanos and one of five on the island.