Speaking in Kazakhstan, British PM says European Union should stretch from the Atlantic to the Urals

David Cameron has said the EU should extend its membership deeper into the former Soviet Union, calling for its borders to run from the Atlantic to the Urals.

Speaking in the former Soviet republic of Kazakhstan on the day that former Yugoslav republic Croatia became the EU's 28th member state, the prime minister hailed the power of the EU to transform divided societies.

Cameron said the membership terms imposed on Croatia and on its former enemy and neighbouring former Yugoslav republic Serbia, which hopes to join in the future, were having a "remarkable" effect in underpinning democracy in the western Balkans.

But the prime minister made clear that he hoped the enlargement of the EU would go further and extend beyond the three Baltic states of Latvia, Lithuania and Estonia – the only former members of the USSR in the EU.

In a question-and-answer session with students at the Nazarbayev University in the Kazakh capital, Astana, the prime minister said: "Britain has always supported the widening of the EU. Our vision of the EU is that it should be a large trading and co-operating organisation that effectively stretches, as it were, from the Atlantic to the Urals. We have a wide vision of Europe and we have always encouraged countries that want to join."

The prime minister did not name any countries. But his remarks indicate that he believes that Ukraine, once known as the bread basket of the Soviet Union, should be admitted to the EU.

Vladimir Putin, the Russian president – who has said that the demise of the USSR was one of the great strategic tragedies of the 20th century – may regard Cameron's remarks as hostile. Putin believes that the EU should extend no further into the former USSR than the Baltic states.

Russia is sensitive about Ukrainian membership of the EU. Ukraine houses the Russian Black Sea naval fleet at Sevastopol, which was in Russia until the Crimean peninsula was gifted to Ukraine by Nikita Khrushchev in the 1950s.

But the prime minister said the EU needs to be reformed as he defended his decision to hold a referendum on Britain's EU membership terms. He said: "We recognise there is a problem in the EU right now that needs to be solved."

Cameron said the EU needed to be more flexible to accommodate euro and non-euro members.

"We have to make this organisation flexible enough to include both sorts of country. In my view the euro countries clearly need to integrate more. If you have a single currency you need to have an integrated banking system, you need to have an integrated fiscal system. You need to make sure you have quite a lot of rules. You need solidarity.

"So you need change in the single currency. And then you need to make the EU more flexible so that it can include countries like Britain or other countries that want to be in this trading, co-operating partnership but don't want the currency.

"That is why I have argued for a renegotiation of the rules of the EU between now and 2017. I have said that, if re-elected, I will hold a referendum by the end of 2017 to give the British people a choice about whether they want to stay in this organisation, which would be changed by then, or to leave this organisation."

The Urals mark the unofficial border between Europe and Asia in Russia. They run north to south and extend into north-west Kazakhstan.

The prime minister is not suggesting the western part of Russia should join the EU. Russia has no interest in joining. But his remarks suggest that all former Soviet republics west of the Urals should be free to apply to join the EU.