What does $10 billion buy? For the oil-rich emirate of Abu Dhabi, which recently came to the rescue of its heavily indebted neighbor Dubai, the answer seemed to be stability as well as political and commercial influence. But the cost of those precious commodities could be set to rise dramatically.

Within days of Abu Dhabi’s December bailout, Dubai renamed its new landmark 160-story tower the Burj Khalifa, in honor of Sheikh Khalifa bin Zayed Al Nahyan, the emir of Abu Dhabi. The assistance also calmed financial markets in the Gulf and around the world. Dubai’s financial condition appears to have deteriorated in subsequent weeks, however, fanning fears of a wider economic fallout in the region and prompting fresh speculation about whether, and under what conditions, Abu Dhabi will provide additional support.

Dubai World, the emirate’s flagship holding company, is seeking to negotiate a standstill agreement with...