The US and South Korea say the exercises are defensive and designed to send a message to Pyongyang that its behaviour is aggressive and must stop.
Tension worsened after North Korea also last week seized a South Korean fishing boat off the east coast in the same area.
Responding to the joint drill, North Korea said the latest exercise was a "dangerous act to light the fuse of a new war".
Tensions have risen sharply since late May when South Korea and the US, citing a multinational investigation, accused the North of torpedoing one of Seoul's warships near the contested border.
The North vehemently denies involvement in the March incident in which 46 sailors were killed.
In his speech to mark the 65th Liberation Day, Lee also proposed a "new paradigm" in relations, urging the North to make a "courageous" change.
Call for unification
The Koreas "cannot afford to repeat the unfortunate history punctuated by mutual distrust and confrontation", he said.
"It is imperative that the two sides choose co-existence instead of confrontation, progress instead of stagnation"
Lee Myung-bak, South Korean president
"It is about time Pyongyang looked straight at reality, made a courageous change and came up with a drastic decision. It should not be afraid of making change," added Lee.
South Korea's Yonhap news agency reportedly quoted Lee on a three-stage plan which includes a proposal for a "unification tax" to prepare for a potentially huge financial burden should the two Koreas unite.
"It is imperative that the two sides choose co-existence instead of confrontation, progress instead of stagnation," Lee was quoted as saying, adding that denuclearisation of the communist neighbour is of the utmost importance.
"The next step is to carry out comprehensive inter-Korean exchanges and cooperation with a view to developing the North's economy dramatically.
"The result will be an economic community in which the two will work for economic integration," Lee said.