The comprehensive Pew Research Center survey conducted between 2008 and 2012 focused on 38,000 people in 39 countries drawn from a global Muslim community of 2.2 billion people.
A solid majority, notably in Asia, Africa and the Middle East, were in favor of sharia -- traditional Islamic law -- being adopted as "the law of the land" in their countries, it found.
"But I would also note that support for making sharia law does vary," said Jim Bell, Pew's director of international survey research.
From 12 percent in Turkey, support for sharia as official national law stood at 56 percent in Tunisia, 71 percent in Nigeria, 72 percent in Indonesia, 74 percent in Egypt and 99 percent in Afghanistan.
But Princeton University professor Amaney Jamal, a special adviser to the Washington-based Pew Research Center, emphasized there is no one common understanding of sharia among all the world's Muslims.
"Sharia has different meanings, definitions and understandings, based on the actual experiences of countries with or without sharia," she said in a conference call with reporters analyzing the findings.
Titled "The World's Muslims: Religion, Politics and Society," the study also revealed many Muslims favor applying sharia in the private sphere to settle family or property disputes.
However, in most countries surveyed, there was less support for severe punishments, such as cutting off the hands of thieves or executing people who convert from Islam to another faith.
A majority of Muslims are also in favor of freedom of religion, even while backing sharia.
In Pakistan, for example, 84 percent of Muslims want sharia enshrined as official law but 75 percent believe non-Muslims are free to practice their religion.
Around half of Muslims in the survey expressed concerns about religious extremism, particularly in Egypt, Iraq and Tunisia.
In most countries, a majority of Muslims said a wife must obey her husband, although a majority also said a woman should decide whether or not to wear a veil.
Most Muslims said they do not feel tension between their religion and modern life, prefer a democratic regime, and enjoy music or Western movies, even if such pastimes are sometimes regarded as undermining morality.
An overwhelming majority viewed prostitution, homosexuality, suicide or alcohol consumption as immoral but there are sharp differences on issues such as polygamy.
Only four percent polled in Bosnia and Herzegovina considered polygamy morally acceptable, against 87 percent in Niger.
A strong majority surveyed said so-called honor killings could never be justified. The only exceptions came in Afghanistan and Iraq, where majorities condoned executions of women deemed to have shamed their families by engaging in premarital sex or adultery.
Violence carried out in the name of Islam was also widely rejected.
In the United States, 81 percent of Muslims said such violence can "never" be justified -- against a global median of 73 percent.
However, substantial minorities in Bangladesh, Egypt, Afghanistan and the Palestinian territories said violence was permissible.