Some Finance Ministry employees, including accountants and national statistics service staff, also walked off the job on Tuesday to protest against wage freezes and allowances cuts. Tax officials will stage a 24-hour walkout on Wednesday.
A lack of popular support for protests so far has offered hope Athens can tackle its fiscal crisis but these protests are some in a series of walkouts that will further test this month the government's resolve to implement its deficit-cutting plan.
The government measures will further cut our salaries, we have already lost 10 percent of our income in the past two years due to wages freezes, said Apostolos Papantonis, treasurer at Greece's customs employees federation.
Customs offices around the country shut down on Tuesday for three days. If the strike lasts longer, it could lead to container pile-ups at ports and border crossings and affect petrol distribution across the country.
Papantonis said the union would decide this week whether to stage more strikes.
Greece's powerful ADEDY public sector union, which held a 24-hour strike last week will join another one-day stoppage by the private sector union GSEE on Feb. 24.
The two unions, which together group half of Greece's 5 million-strong workforce, say the poorest will suffer from a government package designed to bring down the budget deficit from 12.7 percent of GDP last year to under 3 percent in 2012.
Greece shocked markets when the newly elected socialists revealed in October the 2009 budget deficit would be three times higher than original estimates.
Opinion polls show most of Greece's 11 million population back the government.