In the southern port of Vlora, which has been effectively out of government control since last Tuesday, more than 2,000 people marched to the home of a local vegetable store owner who was killed in riots earlier this week.
Only a few uniformed police officers were on the streets, and they made no attempt to break up the march.
The Prime Minister, Aleksander Meksi, has denounced the protests as inspired by extreme leftists and has announced plans for a partial state of emergency that would enable the army to protect Vlora's port and other sensitive zones.
However, the plans have not yet been put into effect, and some members of the ruling Democratic Party fear that the introduction of a state of emergency would merely lead to a bloodbath and revolution.
The protests were sparked by the collapse of pyramid savings schemes in which tens of thousands of Albanians have lost all their money. They have turned into an onslaught on the government partly because many people suspect that Democratic Party officials have benefited from the scams.
Opposition attempts to capitalise on the crisis have met a firm response from the police, who have disrupted all attempts to stage rallies in Tirana. Opposition politicians have been harassed and even physically assaulted.
However, the government has made a small concession by appointing Ethem Kurti, a well-liked native of Vlora, as the city's new police chief.