The Romanian consulate in the Moldovan capital Chisinau is overwhelmed with visa requests from Moldovans.
Romania introduced visa requirements on 1 January, the date it joined the European Union along with Bulgaria.
Moldovans who study in Romania or work abroad have paralysed the consulate's internet site - and it will be unable to clear the backlog before 15 January.
The Romanian foreign ministry says it will boost staff in Chisinau to deal with the applications.
More than 70% of Moldovans speak Romanian and many have family ties across the border in Romania.
Romania has asked the Moldovan authorities for permission to open two new consulates, in the towns of Balti and Cahul.
Moldovans working in EU countries with no embassy in Moldova need to get to Bucharest to renew work permits. Officials say students will get priority.
Correspondents say many Moldovan families rely on money sent back by relatives working abroad.
They say Moldovans resent the restrictions demanded by the EU, as Moldova was part of Romania until the end of World War II, when it was absorbed into the Soviet Union.
Before 2001, Moldovans did not need passports to enter Romania.
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