"This move is not only a grave threat to peace and stability of the Korean peninsula but also to the region," Ri said of the military drills.
He said "there will be physical response against the threat imposed by the United States militarily."
China has harshly criticised the military drills and launched its own naval exercises off its eastern coast.
Calling the new US sanctions "hostile", North Korea said they must be reversed in exchange for a nuclear-free Korean peninsula.
"The sanctions will deepen the hostile policy against the North," Ri said, urging the US to focus instead on resuming stalled six-party talks over the North's nuclear weapons programme and other issues.
'Not a provocation'
Speaking in Washington, PJ Crowley, spokesman for the US state department, said the planned military exercises with South Korea would go ahead.
"It's a defensive exercise meant to improve our ability to work together as allies," Crowley told reporters. "They're not meant as a provocation."
"Actions by North Korea, including the sinking of the Cheonan ... those kinds of provocative steps do in fact pose a threat to security and stability in the region," he added.
South Korea and the US have said the North must admit responsibility for the attack on the Cheonan – which a South Korean-led investigation concluded was sunk by a torpedo fired by a North Korean submarine – before talks can resume.
North Korea has denied any role in sinking the ship, and reiterated the point in bilateral talks on Thursday with Southeast Asian foreign ministers.
After North Korea conducted its second nuclear test last year, the US and others pushed for the North to return to the negotiations, which include South Korea and regional powers China, Japan, the US and Russia.
"If [the US and South Korea] are really interested in the denuclearisation of the peninsula, they should take the lead in helping establish the settings [for restarting talks] before they resume military drills," added Ri.