PM Valdis Dombrovskis says formal application to become 18th eurozone country will be made early next month

Latvia, the EU's third poorest country, is to apply to join the euro within weeks, triggering an east European dash for entry that could push the eurozone to 20 countries from 17 in a few years.

The country's prime minister, Valdis Dombrovskis, said his government would formally apply to join the single currency at the start of next month with the aim of becoming the 18th member by the end of the year. Officials in Riga are consulting with the European commission and European Central Bank.

"It's just a technical issue now," Dombrovskis said. "By July the whole procedure should be finished."

Estonia joined the euro in 2011 at the very height of the currency and sovereign debt crisis – and has prospered ever since. Latvia, recovering from one of Europe's worst financial implosions in 2008-9 that saw the economy contract by a colossal 25%, hopes to emulate their neighbours. The third Baltic state, Lithuania, is expected to apply to join next year.

The Lithuanian prime minister, Algirdas Butkevicius, said: "An action plan has been prepared and a government resolution drafted." The plan is to be finalised this week with a view to joining the euro in 2015 after applying next year.

The debate over joining the single currency is also heating up in Poland. A much bigger country and therefore a much bigger prize or liability for the eurozone, Poland is the only EU country not to have fallen into recession since the Lehman Brothers crash. Increasingly it sees its future in being as closely integrated in the EU as possible, playing the regional leader and usurping Britain's position in policy-making influence.

For that to succeed, euro membership is essential as the zone binds itself into closer political and economic regimes and becomes the key decision-taking forum. The Polish president recently established a high-powered committee to examine and foster eurozone membership. Warsaw is now talking of a 2017 deadline.

It may seem paradoxical or perverse that the east Europeans are increasingly clamouring to join a currency whose survival has hung in the balance for three years. They are seeking stability at a time of the euro's greatest instability.

"We see it as a kind of insurance mechanism," said Dombrovskis. "We don't expect to go back into a crisis. We're sticking with prudent fiscal policies and we don't expect to overheat our economy again.

"And whatever happens to the euro happens to us anyway. Our economy is completely euro-ised: 80% of borrowing, households and businesses, is in euros. This will help financial and economic stability."

Similar arguments are made in Lithuania, while in Poland the impetus is less economic than political and geo-political. Warsaw appears resolved to hitch itself to Germany, and deems it a national security imperative, worried about Vladimir Putin's Russia, to embed itself utterly in the EU. It increasingly sees the eurozone as the safest of havens, despite the volatility.

On the Maastricht rulebook, there is no doubt Latvia passes muster. Its budget deficit was 1.5% of GDP last year, half the 3% ceiling and much better than France or the Netherlands, who will fail to meet their targets this year – not to mention those countries being bailed out. Latvian national debt at 42% of GDP is also well below the 60% ceiling.

Latvia has joined the German chancellor Angela Merkel's fiscal pact and wants to sign up to the ECB banking supervisor currently being negotiated for the eurozone.

"We clearly meet all the benchmarks. We expect the eurozone countries to invite us to join," said Dombrovskis.

Problems remain, however. Public opinion, influenced by the years of crisis at home and in the eurozone, is against giving up the lat, the national currency, by a margin of 3-2 in the polls.

Following the application the European commission and the central bank in Frankfurt have to give a green light amid Latvian worries Brussels may be reluctant because of popular opposition.

Olli Rehn, the monetary affairs commissioner, dismissed such reservations.

"The eurozone could have 18 members by 2014," he said. "There are no criteria related to opinion surveys. You can't be disqualified because of opinion surveys and political criteria."

However, he kept his options open. "Substance is more important than the schedule. I should not create false expectations. We need to assess whether the Latvian economic model is sustainable."

After the recommendations from Brussels and Frankfurt, a final decision will rest with the eurozone governments, where the creditor countries are fed up with bailing out troubled members and may be loath to admit such a poor country, which needed an EU-IMF bailout in 2008. France, in particular, has traditionally resisted various aspects of EU enlargement and the Latvian elite is worried that Paris could be a problem.

And while the issue of Russian money in Cyprus currently complicates the attempt to come up with a eurozone bailout for the partitioned island, there are parallel worries about Russian influence in the former Soviet Baltic state.

Around half of bank deposits in Latvia – a sector dominated by Swedish and Danish banks – are by non-residents, essentially Russian.

"We have a relatively high share of non-resident deposits. It has attracted attention," admitted Dombrovskis.

But some of the Russian capital took flight during the crisis and the banks involved are subject to much stiffer capital and liquidity requirements. Besides, in terms of scale, Latvia comes nowhere near rivalling Cyprus as a financial centre.

For two years, the talk has been of a shrinking eurozone as Greece or others teetered on the brink of being kicked out. That prospect has receded, supplanted by talk of a bigger single currency area.

"A year ago, we said we were sticking to our plan to join," said Dombrovskis. "Other member states said they were waiting. Now that's changing. Lithuania is talking about 2015, the Poles are setting a 2017 target. It would be a strong political signal if the Poles joined."