"I don't expect major problems, our network and the network of our competitors are ready to serve our clients," said a senior official at Piraeus Bank, one of the big four lenders. "There might be lines because many people will want to withdraw money from their deposit boxes," the official said.
After European authorities agreed last week to provide emergency funding assistance, Athens is expected to meet a payment deadline for 4.2 billion euros, including interest payments, due to the European Central Bank on Monday.
VOTE ON WEDNESDAY
Tsipras is eyeing a fresh start and swift talks on the bailout aimed at keeping Greece afloat but he still faces hurdles with parts of the ruling Syriza party in revolt over the tough terms of the bailout agreement.
The Greek parliament approved the bailout package on Thursday but the 40 year-old prime minister was forced to rely on votes from the opposition after 39 rebels from his Syriza party refused to back the government, by voting against or abstaining.
A second vote will be held on Wednesday, on measures including justice and banking reforms, when a similar outcome is expected. However the voting arithmetic is finely poised.
Together with his coalition partners from the right-wing Independent Greeks party, Tsipras has 162 seats in the 300-seat parliament but Thursday's rebellion cut his support to just 123 votes. Under Greek constitutional rules, the minimum support needed for a minority government is 120, so if the number falls below that level, the government's future would be in doubt.
"What worries me is that some people still think that there would be no austerity if we were out of the euro. This argument is absolutely false," State Minister Nikos Pappas, one of Tsipras' closest aides told the leftist Efimerida Ton Syntakton newspaper.
Acceptance of the bailout terms that meant the banks could reopen marked a turnaround for Tsipras after months of difficult talks and a referendum that rejected a less stringent deal proposed by the lenders.
The bailout terms include tax hikes, pension cuts, strict curbs on public spending, an overhaul of collective bargaining rules and a transfer of 50 billion euros of state assets into a special privatisation fund.