“We must punish and retaliate against any provocation by North Korea. That is the most powerful means to deter provocations,” Mr Yoon was quoted as saying in a meeting with his aides, according to his press secretary Kim Eun-hye.
“We must not fear or hesitate because North Korea has nuclear weapons.”
His statement comes days after South Korea’s military said on Monday that it had scrambled fighter jets and attack helicopters and fired warning shots after North Korean drones violated its air space for the first time since 2017.
One drone reportedly also flew over capital Seoul, according to local media reports.
After the intrusion, Mr Yoon lashed out at the country’s military and in particular its failure to bring down the drones while they flew over South Korea for hours.
Also on Monday, the South sent drones over North Korea for three hours in retaliation.
In a statement in parliament, defence Minister Lee Jong-sup said the president had ordered drones to North Korea “even if that means risking escalation”.
South Korea’s military has apologised and said it could not shoot down the drones because they were too small.
The defence ministry also announced on Wednesday that the country will be strengthening its drone capacity.
“We will strengthen our... retaliation capability to be able to destroy key facilities anywhere in North Korea in case of its nuclear attack or use of weapons of mass destruction,” the ministry said in a statement.
The ministry is looking to spend 331.4 trillion won ($261bn) on defence over the next five years.
This year, North Korea has conducted an unprecedented number of missile tests in what some experts call an attempt to improve its weapons and pressure rivals to make concessions such as lifting sanctions in future negotiations.
Last week, the North fired two short-range ballistic missiles on Friday and two medium-range ballistic missiles five days earlier.
Additional reporting by agencies