Restrictions on financial transactions in Cyprus could be fully lifted in a month, according to Foreign Minister Ioannis Kasoulides.
He said this was based on assessments by the country's central bank.
Cyprus imposed capital controls to limit withdrawals and transfers abroad when its banks opened yesterday for the first time since March 16.
They were announced on Wednesday night to prevent worried savers from withdrawing all their money during an acute financial crisis.
The restrictions were imposed for seven days initially and are being reviewed daily.
Across Cyprus, large but orderly lines formed yesterday ahead of the opening of banks for six hours from noon, and guards from private security firms reinforced police outside some ATMs and banks in the capital, Nicosia. No particular crowd issues were reported.
President Nicos Anastasiades expressed his "warm gratitude and deep appreciation towards the Cypriot people for the maturity and spirit of responsibility they have shown at a critical time for the stability of the Cypriot economy," a statement from his office said.
Banks have been shut in Cyprus since March 16 to prevent people draining their accounts as politicians scrambled to come up with a plan to allow the country to qualify for €10bn (£8.5bn) in international bailout loans for its stricken financial sector.
A deal was finally reached in Brussels with other euro countries and the International Monetary Fund early on Monday.
The country's second-largest bank, Laiki, is to be split up, with its healthy assets being absorbed into the Bank of Cyprus. Savers with more €100,000 (£85,000) in both Bank of Cyprus and Laiki will face big losses.
At Laiki, those could reach as much as 80% of amounts above the €100,000 insured limit; those at Bank of Cyprus are expected to be much lower.
The Finance Ministry announced capital controls – to be reviewed daily and initially applying for seven days – to prevent a rush of euros out of the country's banks when they reopened.
They include limiting daily cash withdrawals to €300 (£255) per person and limiting payments abroad to €5,000 (£4,200).