The curfew was lifted from 6 am (0030 GMT) on Saturday until 6 pm. A 24-hour curfew imposed on Monday had been lifted for a few hours on Thursday and Friday to allow the purchase of essential supplies.
The new PM has until now appointed four ministers from the Rajapaksas' Sri Lanka Podujana Peramuna (SLPP).
Wickremesinghe is the sole lawmaker from his United National Party to hold a seat in parliament and is reliant on other parties to form a coalition government.
The main opposition has ruled out supporting him, but several smaller parties have said they would back the new prime minister's policies to stabilise the economy.
However, the new appointments are unlikely to satisfy the protesters demanding the removal of SLPP from power.
More than a month of predominantly peaceful protests against the government turned violent this week after supporters of former Prime Minister Mahinda Rajapaksa stormed an anti-government protest camp in the commercial capital Colombo, burning tents and clashing with protesters and police.
The initial violence and reprisals against government figures also left more than 300 injured.
Following this, Rajapaksa stepped down after violence flared on Monday, leaving his younger brother Gotabaya Rajapaksa to rule on as president.
Hit hard by the pandemic, rising oil prices and tax cuts by the populist government, Sri Lanka is in the throes of its worst economic crisis since independence from Great Britain in 1948.
Useable foreign reserves have dwindled, and rampant inflation and fuel shortages have brought thousands onto the streets in protest.
Post Wickremesinghe's oath-taking ceremony, he had said: "we need to create a country with a future for the youth, where people can eat three meals a day again and free of queues soon."
