Cybersecurity firm CrowdStrike says "a significant number" of devices that were impacted by a global IT outage on Friday are now back online.
In a social media post, the company - whose faulty security update caused Microsoft Windows computers to crash around the world - added it "continues to focus on restoring all systems".
Microsoft has estimated that the incident, which is being described as one of the worst IT outages in history, impacted 8.5m computers around the world.
Businesses, banks, hospitals and airlines were among the worst-hit, with some still struggling to fully restore their systems.
"We understand the profound impact this has had on everyone. We know our customers, partners and their IT teams are working tirelessly and we’re profoundly grateful," CrowdStrike said.
"We apologise for the disruption this has created."
However, the company did not say how many devices were still being impacted.
More than 1,400 flights, into or out of the US, were cancelled on Sunday, according to aviation tracking and data platform FlightAware.
Delta and United Airlines were the worst affected US airlines.
Health services in Britain, Israel and Germany were also impacted on Friday, with some services cancelled.
The massive outage has put a spotlight on the vulnerability of global computer networks, showing how a single glitch can cause global chaos.