The new feature – which Quartz calls 'annotations' – launched today (Tuesday).
Readers can click on a button alongside the paragraphs and post comments, which are post-moderated, and can then choose to share via social media or email.
Once comments have been left, an icon displays the number of contributions, which can then be clicked on to read more.
People can currently login via Twitter or create a Quartz account. Facebook and LinkedIn social logins will be introduced in due course.
The new commenting feature - which is sponsored - is very similar to that created by Medium, the publishing platform which was launched a year ago by Twitter founders Ev Williams and Biz Stone.
Last week we reported how the New York Times was trialling different commenting experiences, and had elevated comments above the line in one particular story.
Zach Seward, a senior editor at Quartz, told Journalism.co.uk the aim of the new feature is to "encourage thoughtful and directed discussion".
He said that "paragraphs act as the discussion prompt" so that people can react to part of the story rather than the article as a whole.
Asked if Quartz had been influenced by Medium, Seward explained that the business title had been toying with above-the-line commenting since before it launched 10 months ago.
He said the design of Medium's 'notes' feature "is really strong and has definitely been an inspiration".
"When Medium rolled out theirs it was an important moment for us," said Seward, explaining that the Quartz team considered the feature as "a testing ground" and followed development closely.
"When we launched we could have slapped on your average comments section to the bottom of the article," Seward said, but that would have been to fulfil expectations rather than to serve a purpose. "A typical comments section wasn't interesting to us," he said.
Seward suggested that this type of commenting feature may become more widely used. "If there's a trend towards annotations," he said, "people have to know what to expect" so there should be some similarities between systems.
He said Quartz will be encouraging comments, with journalists also joining the discussions. They may also post source documents and ask readers to help annotate them.
A release from Quartz explains that some of the earliest newspapers had wide margins for readers to jot down their notes next to articles. "And the web’s technical architects initially planned to include similar annotation functionality across all of the internet," it explains. "It’s in these traditions that Quartz is now empowering readers to engage in discussions in the margins of its articles."
According to the release, Quartz received 5 million unique visitors last month. Around 40 per cent live outside of the US.
A short video which illustrates annotations is at this link.