SEOUL—The short-range missiles tested by North Korea can strike much of South Korea and may be able to carry a nuclear warhead, military experts said, providing Pyongyang with extra firepower as diplomatic frictions grow with Washington.

Pyongyang test-fired a pair of short-range missiles Thursday that soared to a height of 50 kilometers (about 31 miles) before landing in the sea off the country’s east coast. Leader Kim Jong Un directed the test and lauded the weapons’ “long-range strike” capabilities, according to North Korean...