Thousands of Icelanders have rallied outside parliament in Reykjavik demanding the removal of the government following this week's resignation of Prime Minister Sigmundur David Gunnlaugsson over his links to offshore investments.

The daily protests began Monday when opposition leaders introduced a no-confidence motion against Gunnlaugsson, who has since been replaced by the North Atlantic island nation's fisheries minister.

But the opposition is now pressing for a wider no-confidence motion against the entire government, saying two other ministers already have been linked to offshore investments at the center of the global scandal.

Saturday's protesters said Iceland could face an early election or a new coalition government led by the upstart Pirate Party.

"This government is finished," said protester Snorri Asmundsson, a 49-year-old artist who is one of many candidates seeking to become Iceland's president in a June vote. "I give it maybe one week."