By Alistair Scrutton and Mette Fraende

COPENHAGEN (Reuters) - Denmark's centre-left prime minister, accused by her left-wing parliamentary backers of veering too far to the right, said on Friday the country had got through the worst of its economic crisis and should persevere with unpopular reforms.

Elected in 2011 promising to pull Denmark out of an economic slump, Helle Thorning-Schmidt is deeply unpopular half way through her term, opinion polls show, although analysts do not expect her minority government to fall.

"I think we have found the right formula, not to be popular because we have not actually reached that yet, but to do the right thing for the country," the Nordic nation's first woman prime minister told Reuters in an interview.

Denmark, an EU member but euro outsider, has been in recession three times since 2008. The government has downgraded its forecast for economic growth this year four times and now expects the economy to grow by a modest 0.2 percent after a 0.5 percent contraction in 2012.

But consumer confidence is showing early signs of picking up, the housing market is improving and last month's statistics showed faster growth in the second quarter than preliminary figures had indicated.

"We are definitely over the worst," the 46-year-old prime minister said in her office. "We are seeing good figures but we are very cautious not to say that we have exited the crisis."

She said European governments should focus on balancing their budgets and fostering growth, saying it was wrong to blame the European Union, which has advocated austerity measures, for their economic problems, or expect it to fix national problems.

"We have to stay on track, and I think one thing that is very important is, it was never reasonable to blame Europe for the crisis,"

MOOD CHANGE

Denmark has struggled to boost consumer confidence since a property bubble burst in 2007, leaving many people wary of spending. The global financial crisis has also dampened exports, another main driver of the economy.

"We are very cautious to talk about whether we have turned the corner or not ... but we are definitely seeing a mood change in the economy, a mood change in terms of the housing market, consumer confidence and also in terms of our growth figures," Thorning-Schmidt said.

Denmark's public finances and unemployment rate of 6.6 percent put in better shape than many European peers. Its currency, unofficially pegged to the euro, has gained a "safe heaven" reputation during the crisis.

Thorning-Schmidt's three party centre-left minority government has increasingly reluctant backing from the left wing Red Green Alliance.

While the alliance is not expected to withdraw its support for fear of giving power to Conservatives, it regularly accuses her of going too far with free market reforms, including scrapping an early retirement scheme and giving tax cuts to high-earners while trimming Denmark's generous welfare system.

"If we want to have a welfare state where people pay as much tax as they do in Denmark, we also need to make sure that our welfare state is delivering," Thorning-Schmidt said.

A strong advocate of the European Union and former European parliament member, she said she had not given up on Denmark joining the euro, even though support for the common currency is at a record low due to the euro zone's debt crisis.

Danes voted against adopting the euro in 2000 and successive governments have since postponed putting the question again.

"There is no point having a referendum at this stage because there are still so many discussions about where the euro is going - will there be treaty changes, what is happening to the banking union, all these things," Thorning-Schmidt said.

"But if you are asking if we have given up on ever becoming a member then the answer is 'No, we have not'."

(Editing by Paul Taylor and Philippa Fletcher)