Prime Minister Geir Haarde has so far vowed to stay on despite the mounting protests, saying a snap election would disrupt efforts to stabilize an economy rocked by the collapse of Icelandic banks in the face of global financial turmoil.
His office declined to comment on Gunnarsdottir's statement.
Anti-government protests have become regular fixtures in Iceland since its financial system disintegrated in October after a decade-long boom fuelled by cheap foreign funding.
Protests turned violent in the early hours of Thursday, with demonstrators hoping to oust Haarde, the central bank governor and other senior officials over what they see as "incompetent rule" and cozy ties to the business elite.
Haarde, whose limousine was pelted with eggs and cans by demonstrators on Wednesday, did not discuss the issue of an early election during a speech to parliament earlier on Thursday, which focused on measures to bolster the economy.
Icelandic police used tear gas to quell anti-government protesters who injured two policemen overnight.
"There were a couple of hundred (protesters) when they had to use the gas," police spokesman Gunnar Sigurdsson said. "It went on for two hours or so. There were no arrests. Some injuries, but not serious."
At midday on Thursday, about 30 protesters were demonstrating, chanting for the "disqualified government" to resign and more rallies were planned for later in the day.
Latvia, Bulgaria and other European countries hit hard by the global economic meltdown have also seen unrest.