A South Korean defense official was quoted by the Yonhap news agency as saying the budget request was intended to "drastically strengthen [the] missile arsenal to cope with threats by North Korea."
North Korea early this year agreed to place a moratorium on long-range missile and nuclear tests in exchange for substantial food assistance from the United States. That deal collapsed in April, however, when Pyongyang attempted to send a satellite into orbit using a long-range rocket.
Strained relations between Pyongyang and Seoul soured after the North Korean government accused its southern neighbors of insulting the legacy of Kim Il Sung, the country's founder.
North Korea was said to be preparing for a test of a nuclear device following the failed rocket launch in April.
Authorities at Jane's Defense Weekly told Yonhap that information gleaned from satellite imagery suggested North Korea was working at a suspected nuclear test site in the country's northeast.
Glyn Davis, U.S. special envoy for North Korean policy, said a nuclear test by North Korea would be a serious mistake.
"If there is further provocation such as a nuclear test, there will be swift and sure reaction by the international community," he was quoted as saying.