"Let's make Greece a full success story inside the euro zone ... reduce unemployment, particularly among the young," Moscovici told reporters in translated comments after meeting Greek Prime Minister Alexis Tsipras in Athens.
"Greece should regain full market access," he said.
Greece, which emerged in August from its third international bailout since 2010, has tested market appetite under the watch of its international lenders in recent years. Now, it wants to return to bond markets as a regular borrower.
Under its post bailout surveillance, Greece has also agreed to continue structural reforms under quarterly scrutiny from the European Commision. Those reforms include tackling a mountain of bad loans burdening its banks and privatisations.
Moscovici urged Greece to keep up its efforts so that euro zone finance ministers, known as the Eurogroup, issue a positive assessment in March and approve a first payment of about 750 million euros (£664.7 million) from profits ECB has made on Greek bond holdings, the so-called ANFA and SMP profit returns.
"Let's make this second post-programme review a success. That's my message and that's what we are working (towards) today," Moscovici said after meeting Greek Economy Minister Yannis Dragassakis.
(Reporting by Angeliki Koutantou; Additional reporting by George Georgiopoulos; Editing by Catherine Evans)
