Greek Prime Minister Alexis Tsipras is meeting members of his Syriza party to try to rally support, ahead of a second vote in parliament on reforms needed as part of a planned bailout.
The BBC said the country's public sector union was calling for more protests.
After the austerity measures passed last week, these reforms are of a more structural nature.
They include legislation to ensure that, if a bank fails, the shareholders and creditors will take a loss, as well as an overhaul of Greece's judicial system.
More contentious measures - phasing out early retirement and tax rises for farmers - have been pushed back to August.
The BBC's Mark Lowen said the reforms were likely to pass, thanks to opposition support, but Mr Tsipras would again expect a rebellion within his party.
The measures are a condition for Greece to wrap up negotiations on the bailout deal, which it hopes to conclude by 20 August.