"We're yet to see how stable the new connection is," Jim Cowie, chief scientist for the company, said in a telephone call after the services were restored.
"The question for the next few hours is whether it will return to the unstable fluctuations we saw before the outage."
Meanwhile South Korea, which remains technically at war with the North, said it could not rule out the involvement of its isolated neighbor in a cyberattack on its nuclear power plant operator. It said only non-critical data was stolen and operations were not at risk, but had asked for U.S. help in investigating.
South Korean President Park Geun-hye said on Tuesday the leak of data from the nuclear operator was a "grave situation" that was unacceptable as a matter of national security, but she did not mention any involvement of North Korea.
Read MoreNorth Korea goes completely offline: Report
North Korea is one of the most isolated nations in the world, and the effects of the Internet outage there were not fully clear.
Very few of its 24 million people have access to the Internet. However, major websites, including those of the KCNA state news agency, the main Rodong Sinmun newspaper and the main external public relations company went down for hours.
Almost all its Internet links and traffic pass through China, except, possibly, for some satellite links.
"North Korea has significantly less Internet to lose, compared to other countries with similar populations: Yemen (47 networks), Afghanistan (370 networks), or Taiwan (5,030 networks)," Dyn Research said in a report.
"And unlike these countries, North Korea maintains dependence on a single international provider, China Unicom."
No proof, China says
The United States requested China's help last Thursday, asking it to shut down servers and routers used by North Korea that run through Chinese networks, senior administration officials told Reuters.
The United States also asked China to identify any North Korean hackers operating in China and, if found, send them back to North Korea. It wants China to send a strong message to Pyongyang that such acts will not be tolerated, the officials said.
By Monday, China had not responded directly to the U.S. requests, the officials added.