The case is being closely watched by other countries wrestling with similar concerns, including members of the European Union. A ruling is due by the end of June.
A 2016 decision by the New York-based 2nd U.S. Court of Appeals siding with Microsoft marked a victory for tech firms that increasingly offer cloud computing services in which data is stored remotely. President Donald Trump's administration appealed that ruling to the Supreme Court.
Globally dominant American tech companies have expressed concern that customers will go elsewhere if they think the U.S. government's reach extends to data centers all around the world without changes being made to the law.
Microsoft, which has 100 data centers in 40 countries, was the first American company to challenge a domestic search warrant seeking data held outside the United States.
Brad Smith, Microsoft's president and chief legal officer, told reporters last week the U.S. government should not be able to act unilaterally to access such data without taking into account the laws and interests of other countries.
"It's more likely to be a recipe for international tension and chaos," Smith said.
Solicitor General Noel Francisco, the administration's top lawyer in Supreme Court cases, said in court papers that a ruling for Microsoft "would hamper domestic law enforcement and counterterrorism efforts."
If the Supreme Court were to rule in favor of Microsoft, the government could still gain access data held overseas, but the process would be more cumbersome and potentially take longer.
Lawmakers are considering making changes to the 1986 law.
Bipartisan legislation has been introduced in Congress to update the statute, a move backed by both Microsoft and the administration. The measure would let U.S. judges issue warrants while giving companies an avenue to object if the request conflicts with foreign law. If Congress were to pass the bill before the Supreme Court rules, the case would likely become moot.
Though Microsoft is based in the United States - Redmond, Washington, to be precise - the appeals court said the emails were beyond the reach of domestic search warrants obtained under a 1986 U.S. law called the Stored Communications Act.
The Microsoft customer whose emails were sought told the company he was based in Ireland when he signed up for his account.
Other companies including IBM Corp IBM.N , Amazon.com Inc AMZN.O , Apple Inc AAPL.O , Verizon Communications Inc VZ.N and Alphabet Inc's GOOGL.O Google filed court papers backing Microsoft. Google has mounted challenges similar to Microsoft's.
The administration has the support of 35 states led by Vermont who say they routinely seek access to data stored overseas, especially in cases involving child pornography.
Several foreign governments, including Ireland and Britain, filed court papers raising concerns about the U.S. government's position.
Ireland's government said in its brief that the question of how law enforcement authorities can access such information is already covered by a 2001 treaty with the United States that allows for information sharing and enforcement of court orders.
The treaty's procedures "represent the most appropriate means to address requests such as those which are the object of the warrant in question," Ireland's brief said.
The European Commission, representing the 28-country European Union, filed a brief saying that when a country is seeking data from outside its jurisdiction "the interests and laws of that foreign jurisdiction must be taken into account."
The Supreme Court has ruled twice in recent years in major cases concerning how criminal law applies to new technology, both times ruling against law enforcement. In 2012, the court held that a warrant is required to place a GPS tracking device on a vehicle. In 2014, the court ruled that police need a warrant to search a cellphone seized during an arrest.
In the court's current term, which ends in June, the justices are due to rule on another privacy issue on whether police need search warrants to access cellphone location information held by wireless carriers. Based on the Nov. 29 oral argument, the justices appear likely to rule against law enforcement again.
(Reporting by Lawrence Hurley; Editing by Will Dunham) ((email@example.com; Twitter: @lawrencehurley; +1 202-809-3080))