President Lee Myung-Bak at a ministerial meeting on April 28 approved a USD 2.14 billion defence ministry project to buy 500-600 new missiles, Chosun Ilbo newspaper said.
Yonhap news agency carried a similar report.
The defence ministry declined to confirm the reports, saying only that South Korea "agrees on the necessity of bolstering its missile capability".
The meeting followed North Korea's long-range rocket launch on April 13 and its repeated threats against the South's conservative government.
The defence ministry made its request "given the mounting threat of provocations from the North since (new leader) Kim Jong-Un took power", Chosun Ilbo quoted a government source as saying.
On April 19, the South unveiled a new cruise missile dubbed the Hyunmu-3 with a range of up to 1,500 kilometres, capable of destroying targets such as missile and nuclear bases anywhere in the North.
Chosun said the military wants to increase the number of its Hyunmu-3 cruise missiles, and the number of Hyunmu-2 ballistic missiles which have a 300 km range.
It said they would be used to knock out the North's nuclear weapons facilities, Rodong and Scud missile bases, biochemical weapons plants, command facilities and air force bases in the early stage of any war.
Military officials say the North has about 800 road-mobile missiles. Some 600 are Scuds capable of hitting targets in South Korea, and possibly Japanese territory in some cases.
There are another 200 Rodong-1 missiles that could reach Tokyo.