Both tests were believed to be of a much-hyped, intermediate-range Musudan missile capable of reaching US bases as far away as Guam.
The US State Department strongly condemned the launches, saying they represented clear violations of UN resolutions banning North Korea from any use of ballistic missile technology.
The first test shortly before 6:00 am (2100 GMT Tuesday) was deemed to have failed after reportedly flying around 150 kilometres (90 miles) over the East Sea (Sea of Japan).
The South Korean defence ministry said the second Musudan — fired from the same east coast location two hours later — had flown 400 kilometres.
“South Korea and the United States are conducting further analysis,” the ministry said in a statement that stopped short of labelling the second test a success or failure.
North Korea had previously carried out four failed Musudan tests this year, all of which either exploded on the mobile launch pad or shortly after take-off.
A successful test would mark a major step forward for a weapons programme that ultimately aspires to develop a proven nuclear strike capability against the US mainland.