Greek banks have reopened after a forced three-week closure - but restrictions on transactions, including cash withdrawals, remain.
Many goods and services will also become more expensive as a result of a rise in VAT approved by parliament last Thursday, among the first batch of austerity measures demanded by Greece's creditors.
Parliament also agreed to deep reforms in the pension system including a gradual phasing out of all early retirement options.
In a decree on Saturday, the Greek government kept the daily cash withdrawal limit at 60 euros but added a weekly limit. That means a depositor who does not withdraw cash today can withdraw €120 tomorrow, and so on, up to €420 a week.
Bank customers will still not be able to cash cheques, only deposit them into their accounts, and will not be able to get cash abroad with their credit or cash cards and can only make purchases. There are also restrictions on opening new accounts or activating dormant ones.
The decree also pushes back by a month, to August 26, the deadline for filing income tax returns.
The order came on the same day as Greece's coalition government swore in its new, reshuffled cabinet.
Five prominent dissidents from the radical left Syriza party, the senior coalition party, were replaced. Four of them had voted against an agreement with Greece's creditors on Thursday and the fifth had resigned before the vote.
The most urgent business for the reshuffled government is to pass another batch of austerity measures by Wednesday or early Thursday.
Among the goods that Greeks will find more expensive today are some meats, coffee, tea, cooking oils other than olive oil, cocoa, vinegar, salt, flowers, firewood, fertiliser, insecticides, sanitary towels and condoms. All these will see the VAT rise from 13% to 23%.
Services whose VAT also goes up from 13% to 23% include restaurants and cafes, funeral parlours, taxis, cramming and tutorial schools - very popular with Greek students who want to make up for the deficiencies of the school system - language institutes and computer learning centres. Public transport fares are expected to rise early next month.
Greece closed its banks from June 29 to prevent a bank run after the European Central Bank did not increase emergency funding as Greece's second bailout expired.
After the Greek parliament passed an agreement on Thursday to seek a third bailout and related austerity measures demanded by creditors, the ECB raised its emergency funding to the cash-strapped Greek banks.
On Friday, German MPs voted 439-119 in favour of opening discussions on Greece's third bailout and the EU decided to release a short-term loan of €7.16 billion to help Greece pay back a loan due today to the ECB plus arrears owed to the International Monetary Fund.