TOKYO—Worried by a sharp slowdown in the economy and a strong yen, Japan's government is considering another round of stimulus to stoke growth as measures enacted during the recent financial crisis begin to expire.

But policy makers face a daunting challenge balancing any new spending with their pledges to curb the country's debt, which is already approaching twice the size of Japan's gross domestic product. Economic growth slumped in the quarter ended in June to an annualized pace of 0.4% from 4.4% in the previous quarter, and tax revenue will likely take a hit as a result.

The government is unlikely to add to its mountain of debt to finance any new steps, which will probably be limited in scope and in long-term impact, analysts say.

The government is now seriously considering where to spend limited tax revenue in order to promote "economic expansion," Finance Minister Yoshihiko Noda said Thursday. "If we had lots of tax [revenue] or lots coming in, we could do anything, but that is not the case," he said.

Mr. Noda said he thinks it's time to carefully consider how to create conditions for "young people to have dreams and get jobs." The remarks come after Prime Minister Naoto Kan earlier in the week called the jobs market for young people "very bleak."