The comments came hours after the South, which hosts 28,500 US troops, said it wanted to reopen a channel of dialogue with North Korea, as Moon seeks a two-track policy involving sanctions and dialogue to try to rein in its neighbor.
Pyongyang has made no secret of the fact it is working to develop a nuclear-tipped missile capable of striking the US mainland, and has ignored international calls to halt its nuclear and missile programs - even from China, its lone major ally.
It conducted its latest ballistic missile launch - in defiance of UN Security Council resolutions - on Sunday, which it said was a test of its capability to carry a "large-size heavy nuclear warhead," drawing council condemnation.
"The reality is that there is a high possibility of a military conflict at the NLL (Northern Limit Line) and military demarcation line," Moon was quoted as saying by the presidential Blue House.
He also said the North's nuclear and missile capabilities seem to have advanced rapidly recently, but that the South was ready and capable of striking back should the North attack.
Moon won an election last week campaigning on a more moderate approach towards the North, and said after taking office that he wants to pursue dialogue as well as pressure.
The United States said earlier it believed it could persuade China to impose new UN sanctions on North Korea, and warned that Washington would also target and "call out" countries supporting Pyongyang.
US President Donald Trump warned this month that a "major, major conflict" with North Korea was possible, and in a show of force, sent the nuclear- powered Carl Vinson aircraft carrier strike group to Korean waters to conduct drills with the South and Japan.