On Sunday a report by Iceland's Meteorological Office and University of Iceland scientists classed the eruption as "dormant".
Experts are expected to closely monitor the volcano, which began erupting on April 14, very closely in the days and weeks to come.
Danger to airliners from the volcanic ash plume led most northern European countries to shut their airspace April 15-20, grounding an estimated 10 million travellers worldwide.
Smaller-scale disruptions have continued since then, as the volcano produced more ash.
Experts have cautioned that once the current eruption halted, a new blast in another crater or in the neighbouring and much larger and fiercer Katla volcano might follow.
When or if that will happen is also, according to Gudmundsson, "impossible to say."
In recent days, experts had said the activity at Eyjafjallajokul, which peaked for a third time just over a week ago, had slowed significantly.
Gudmundsson however said it was difficult to tell exactly when the activity had stopped.
"The flow of magma was very small yesterday, but it was still erupting at 5:00 to 6:00 pm (1700-1800 GMT). Ash was falling to the west of the volcano," he said.
The last time the volcano awoke, in 1821, it erupted on and off for almost two years.