More than 100,000 Moldovans already hold Romanian passports
The EU will this week launch talks with six Eastern European neighbours on closer relations - including Moldova, which only last month was rocked by violence following a disputed election.
Moldova is Europe's most impoverished country and its 4.1 million people can only travel to the EU if they have a special visa. But Romania has offered passports to up to one million Moldovans - alarming both Moldova and some in the EU, says the BBC's Oana Lungescu.
Step into the ornate building of the central post office in the Moldovan capital, Chisinau, and you see small crowds of people huddling around a big marble-topped table.
Each one is filling out an application for Romanian citizenship. Dozens more queue up to get the forms; others wait in line to post them to the Romanian embassy.
"It's because we haven't got work here," one woman says. "We want to look for work in Romania or Europe. With a Romanian passport it's going to be easier."
A young man in the queue says a Romanian passport is "a chance to see the world".
"I want to raise my family in Moldova, but I also want to travel, meet new people," he adds. "This is my future."
Around 1,000 people a day have come to the post office in the past few weeks, since Romania changed its citizenship law to speed up procedures for Moldovans, following the violent anti-government riots that erupted in the former Soviet republic last month after a disputed election.
The change was initiated by President Traian Basescu in an unusual tit-for-tat move after his Moldovan counterpart, Vladimir Voronin, accused Romania of backing the protesters, expelled its ambassador and re-introduced visa requirements for Romanians.
Moldova's president accused Romania of stoking the protests last month
Mr Basescu said he could not allow "a new Iron Curtain" to descend on the border with Moldova, most of which was part of Romania until it was annexed by the Soviet Union in 1940.
The decision may be political bluster ahead of Romania's presidential election later this year, but some commentators said Mr Basescu was trying to leave Mr Voronin "without people".
The changes are clear enough.
The language test has been scrapped, as Moldovan is practically the same as Romanian anyway. Anyone with a great-grandparent who was once a Romanian national can apply and expect an answer within five months.
Until now, only a few thousand requests were approved every year - so envelopes have been piling up at the Romanian embassy in Chisinau.
Speaking on Romanian TV, President Basescu said there were 650,000 envelopes, but some enclosed several applications.
He estimated the number of those who wanted to become Romanian citizens at up to one million, a quarter of Moldova's population.
Outside the embassy, there is hope, uncertainty - more people waiting in line.
Nadia Codreanu, an accountant, sent her request in 2002.
"I really hope it will be easier, and that in half a year I will get the Romanian passport," she says.
"Moldovans feel Romanian because you can't just forget many centuries of common history and say we have nothing in common with Romania".
What she does with her passport will depend on what happens in Moldova.
If the authorities increase pressure on the pro-Western opposition, Nadia explains, she may leave the country.
More than 100,000 Moldovans hold Romanian passports, but even more are believed to have Russian citizenship, especially in Moldova's breakaway region of Trans-Dniester, which enjoys Moscow's backing.
Despite almost two decades of independence, Moldovans still appear divided about who they are and whether their country should get closer to Russia or the West as it grapples with a deepening economic and social crisis.
For Vladimir Turcanu, an MP from the ruling Communist Party, it is not a question of identity, but of outside intervention.
"This mass granting of the Romanian citizenship is a way to assimilate the Republic of Moldova," he says.
"We see it a threat to the statehood, a threat to the integrity and sovereignty of our country."
Under EU laws, Romania is entitled to give citizenship to anybody it likes, just as Spain granted legal papers a few years ago to 600,000 irregular migrants.
Spain also allowed citizenship applications for up to 500,000 descendents of people who went into exile after its civil war.
Mr Diaconescu said applications would be considered on an "individual basis"
But it is Romania's move that has triggered most concern.
Senior EU diplomats call it unwise, risky and destabilising.
Amid fears that up to a million impoverished migrants could enter Europe through the back door, Romanian Foreign Minister Cristian Diaconescu reassured other EU members on Friday that decisions would be taken on a case-by-case basis and that many people would not qualify.
Romanian diplomats say only 20,000 cases are in the pipeline, because many Moldovans have failed to complete the complex application procedures.
Whatever the figures turn out to be, there is a clear risk that Moldova, already weakened by the conflict in Trans-Dniester and an economy on the brink, could become a chronic source of instability on Europe's eastern border.
The EU envoy for Moldova, Kalman Mizsei, thinks the real answer would be to allow all Moldovans to travel to the EU without a visa.
One market trader said all seven of her children had left to work abroad
"Moldova's situation," he says, "differs from any other and therefore we, the European Union, also need to have bold initiatives here that would give the perspective of a visa-free situation for the Moldovans."
"That's an issue of core importance for Moldova as a state."
It is not a call that EU interior ministers want to hear.
Germany and others say Moldova has little prospect of visa-free travel for the next three to five years.
But one million Moldovans have already left, often without legal papers, in search of work and a better future. It is an unparalleled exodus.
In Chisinau's bustling market, an old woman selling a few bunches of parsley told me that all seven of her children had left to work in Romania, Italy and Russia.
It is a story you hear across the country. For with or without Romanian passports, Moldovans are choosing to vote with their feet.