"All the other reforms will come from this one. Coming up with good laws is useless if they cannot then be implemented," Padoan said at a press conference in Rome.
The public administration reform promoted by Prime Minister Matteo Renzi's government is currently being debated in parliament.
"Italy's growth is still weak and has to be reinvigorated with all-out structural reforms," Padoan said, after gross domestic product shrank by 0.1 percent in the first quarter.
He said Italy's privatisation programme, which according to some estimates could raise up to €12 billion a year, would add 0.7 percentage points to GDP growth per year.
Padoan said the key theme for Italy's presidency of the European Union starting next month would be "jobs and growth" and called the ongoing debate over the need or not for budget austerity "sterile and even dangerous".
He said Italy will focus on improving the EU's internal market, structural reforms and financing growth, as well as measures to ensure long-term investment in Europe's economy.
"I want concrete results to help the next European Commission," said Padoan, a former chief economist at the Organisation for Economic Co-operation and Development.
The new Commission is due to take office next month.