By Stephen Nakrosis

Payments services company Square Inc. said Wednesday it would begin to offer On-Demand Delivery for the Square Online Store.

"With On-Demand Delivery, Square Online Store sellers can dispatch a courier through delivery partners for orders placed directly on their website," the company said. "Sellers can get started with On-Demand delivery powered by Postmates now, with additional delivery partners coming soon."

With its new offering, Square said, a courier from a restaurant's delivery partner is dispatched when an order is placed on the seller's online store. "Sellers pay a flat fee of $1.50 per order to Square, plus a fee to their delivery partner that is calculated in real-time based on distance and other factors," the company said.

When orders are placed through Square Online Store, sellers receive contact information in the Square Customer Directory, the company said, adding that when paired with other products like Square Marketing and Square Loyalty, sellers can strengthen customer relationships, create open lines of communication, and incentivize patrons to keep coming back.

Square said processing will be free on all on-demand delivery orders through July 8 for up to $50,000 in sales. The company is also waiving dispatch fees until July 1.

--Write to Stephen Nakrosis at stephen.nakrosis@wsj.com