SIMFEROPOL, Ukraine — With thousands of heavily armed Russian troops occupying this perennially embattled peninsula, an overwhelming majority of Crimeans voted on Sunday to secede from Ukraine and join Russia, resolutely carrying out a public referendum that Western leaders had declared illegal and vowed to punish with economic sanctions.

The outcome, in a region that shares a language and centuries of history with Russia, was a foregone conclusion even before exit polls showed more than 93 percent of voters favoring secession. Still, the result deepened the conflict over Ukraine, forcing the United States and its European allies to decide how swiftly and forcefully to levy threatened sanctions against Russian officials including top aides to President Vladimir V. Putin.

With the voting complete, Mr. Putin, who had stalled on the question of annexation by saying he wanted to hear the Crimean public proclaim its will, is now under pressure to make a decision. He could move ahead — a complex and costly venture given the peninsula’s geographic isolation — or leave more than two million people, whose well-being he vowed to protect, in the limbo of other Russian-backed breakaway regions like Abkhazia and South Ossetia, in Georgia.

Should he annex Crimea, Mr. Putin could find himself quickly forced into negotiations with the fledgling government in Kiev that he has so far refused to recognize or meet, or face a serious conflict over water, energy and other essentials for which Crimea is largely dependent on mainland Ukraine.