STOCKHOLM—Sweden's central bank surprised markets by cutting a key interest rate deeper into negative territory, underscoring the limited monetary-policy options for European countries outside the dominant eurozone.

The persistent economic weakness in the eurozone—and a massive stimulus program launched by the European Central Bank earlier this year—has left the currency bloc's neighbors little alternative but to follow the ECB's lead. That comes despite worries, from Scandinavia to Switzerland, that healthy economic growth and low borrowing rates are leading to unsustainable price increases in housing and other sectors.

Economic turmoil in Greece is complicating the task of European central banks outside the eurozone even more by lifting demand for assets in countries that investors perceive as safe. That, in turn, is pushing up their national currencies and threatening exports.

Faced with these diverging prospects, Sweden's central bank, the Riksbank, cut its main policy rate to a record low of minus 0.35%. It also extended its bond-buying program by $5.37 billion.

A key reason: the ECB's massive quantitative easing program—which will pump more than €1 trillion ($1.11 trillion) in freshly minted money into financial markets by September 2016—has sparked a flood of money into the Scandinavian economies and forced policy makers to effectively match the ECB's stimulus or risk soaring currency values.

For these small, open economies, "you are influenced in what's going on with your big neighbor," said Paul De Grauwe, professor at London School of Economics.

There is another factor at work too: Greece, whose uncertain future as a euro member has roiled financial markets. For countries such as Sweden, being outside the eurozone would appear to be a blessing: It has much less financial exposure than Germany and others in the euro bloc, and doesn't have to be involved in many of the high-stakes crisis summits.

But they still face challenges. With Greece in crisis, global investors are more likely to seek havens, driving up Sweden's krona and Switzerland's franc. At a news conference, Riksbank Gov. Stefan Ingves said his country's growth looked set to take off next year but the crisis in Greece had "substantially increased the uncertainty" over the prospects for overseas growth.

If the Swedish krona were to strengthen considerably it would make the Swedish central bank's task of boosting inflation to its target of 2% all but impossible as imports would become cheaper. Swedish inflation is currently running at 0.1%.

Meanwhile, both Denmark and Switzerland have cut deposit rates to record lows of minus 0.75% despite solid economic prospects. Denmark aims to keep its currency, the krone, pegged to the euro to provide stability for exporters and keep inflation low. Switzerland's central bank had set a ceiling on the franc's value against the euro for more than three years but abandoned it in January, sending the franc soaring. The Swiss central bank intervened in currency markets this week after Greece's crisis escalated.

Yet these measures are for economies that are fundamentally strong. The unemployment rate was 7.7% in Sweden last month and 6.2% in Denmark, versus 11.1% in the eurozone.

In short: they are exercising a crisis-like monetary policy, just without the crisis.

But concerns are rising that the monetary policies taken recently could create problems for the future by fueling destabilizing asset bubbles, particularly in housing.

Sweden suffered through a burst debt bubble in the early 1990s and Denmark's housing market crashed about a decade ago. Some economists say there are fresh signs that these bubbles are forming again and officials are starting to worry their policies are a root cause. They hope that regulatory policies can prick any bubbles before they get dangerously large.

Data released Thursday showed Swedish house prices in Stockholm rose 15% on the year in the second quarter and builders are struggling to meet demand for new apartments.

The noise of hammering can be heard at Vä llingby Parkstad, a redevelopment of the old headquarters of the state-owned power company Vattenfall AB on the western edge of Stockholm. When Vattenfall moved out in 2012 the cranes and earth movers arrived. Apartments have been selling fast since they went on sale last year.

Olga McLeod, a 30-year-old medical researcher, braved rain with her two children to view an apartment on a recent Sunday. "It is really tough. Prices go up so quickly and you need to go through the bidding and it is stressful. You expect one price and then it goes up 500,000 Swedish kronor [$60,000] and you are out of your range," she said.

A similar pattern can be seen in Denmark.

On a recent day in Copenhagen, Soren Felden Nielsen, the chief commercial officer for a Danish property developer, checked progress at the Carlsberg City project, a residential and commercial area that his company is building near the city center.

When Carlsberg, the world's fourth largest brewer, halted production here in 2006, it left a prime location for redevelopment. But nothing happened on the 330,000-square-meter site until 2012, when the economy began to pick up again after a sharp slowdown during the financial crisis.

Mr. Felden Nielsen said 32 apartments on a block called Humlehuset had been put up for sale for between 2.095 million Danish kroner ($312,007) and 2.895 million Danish kroner ($431,150).

All the apartments in Humlehuset were reserved within 24 hours of being released to the market, he said.

He said he was sanguine about the risks, saying the sharp price rises in Copenhagen are underpinned by a lack of housing stock and migration into the capital. He saw potential for further price rises, albeit at a slowing pace, even if interest rates move higher.

At the Riksbank, Mr. Ingves has struck a bleaker tone. "If you look at the history of this country, there are usually 30 years between crises," he said in a recent speech. "That is about the amount of time it takes for people to forget. We have another five to go."

Write to Charles Duxbury at charles.duxbury@wsj.com and Brian Blackstone at brian.blackstone@wsj.com

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