In a blog post, the company said it would focus on services such as gaming tool Xbox Live, the consumer version of its Outlook email service, and its consumer documents-sharing service.
But for its search engine Bing, Microsoft cited free expression and said it would remove links only when that "is required of search providers under local law".
Initially, Microsoft will rely on consumers to report objectionable content.
The company also said it would fund research of a tool that scans content and flags images, audio and video.
"We will consider terrorist content to be material posted by or in support of organisations included on the Consolidated United Nations Security Council Sanctions List that depicts graphic violence, encourages violent action, endorses a terrorist organisation or its acts, or encourages people to join such groups," the blog post said.
The steps illustrate the tough predicament many companies face balancing public safety with individual rights.
The issue came to the fore after Apple and the US Government clashed over whether federal authorities could force Apple to create software to unlock a phone used by a shooter in the San Bernardino attacks last year.
Ultimately, the Government paid a third party to unlock the phone.
"The events of the past few months are a strong reminder that the Internet can be used for the worst reasons imaginable," Microsoft said in its post.
Microsoft said users could use an online form to recommend removal of content.
It said it would provide information on how to counter negative content, a policy also adopted by Facebook.
The social-media service this year announced a tool it calls "counter speech," encouraging activists to counter extremist views with posts promoting tolerance.
Last year, Facebook updated its guidelines to prohibit advocacy of "terrorist activity, organized criminal activity or promoting hate".
Between mid-2015 and early 2016 Twitter suspended 125,000 accounts, most of which it believed were linked to the militant Islamic State group.