The widening gaps in Greece and Italy, although expected, are seen as stretching EU fiscal rules that require countries with high debts to gradually bring them down.
The overall debt in the 19-country currency bloc fell to 85.1 percent of gross domestic product (GDP) last year from 87.1 percent in 2017, Eurostat said.
The bloc's aggregated budget deficit also dropped to 0.5 percent of GDP from 1.0 percent in 2017.
The fall coincided with Germany's reduction of its debt to 60.9 percent of GDP from 64.5 percent. The bloc' largest economy also widened its public surplus to 1.7 percent of output from 1.0 percent in 2017.
But in Greece, the debt climbed to 181.1 percent of GDP in 2018, the largest ratio in the euro zone.
The increase from the 176.2 percent figure Athens posted in 2017 was mostly due to the last instalment of euro zone creditors' loans as part of the country's third bailout programme which ended last summer.
The bailout programme exempts Greece from the normal application of EU rules that require cuts of public debt by 1/20th a year of the excess above the 60 percent of GDP upper debt threshold allowed by EU law.
Italy, whose eurosceptic government embarked last year on free-spending plans with little impact on growth, has seen its debt grow to 132.2 percent of its output in 2018 from 131.4 percent in the previous year.
The European Commission, in charge of monitoring euro zone states' budgets, refrained in December from starting disciplinary steps against Italy's over its growing debt.
But it then predicted that the debt would be at 131.1 percent of Italian GDP in 2018.
The Commission has said it would against assess Rome's compliance with EU fiscal rules, including the requirement to cut debt, in June after taking into account the final debt data from Eurostat, its own forecasts for debt developments due in May and Italy's report on fiscal plans for the next three years.