Mattis' comments did not go beyond his recent statements of concern about North Korea, although he appeared to inject a stronger note about the urgency of resolving the crisis.
While he accused the North of 'outlaw' behavior, he did not mention that President Donald Trump has ratcheted up his own rhetoric.
In August, Trump warned the North not to make any more threats against the US and said that, if it did, it would be met with 'fire and fury like the world has never seen.'
The North says it needs nuclear weapons to counter what it believes is a US effort to strangle its economy and overthrow the Kim government.
South Korea's conservative politicians have also called for the US to bring back tactical nuclear weapons that were withdrawn from the Korean Peninsula in the 1990s, which they say would make clearer the US intent to use nukes in a crisis.
But Mattis and Song were strongly dismissive of the idea.
'When considering national interest, it's much better not to deploy them,' said Song, adding that the allies would have 'sufficient means' to respond to a North Korean nuclear attack even without placing tactical nukes in the South.
Trump entered office declaring his commitment to solving the North Korea problem, asserting that he would succeed where his predecessors had failed.
His administration has sought to increase pressure on Pyongyang through UN Security Council sanctions and other diplomatic efforts, but the North hasn't budged from its goal of building a full-fledged nuclear arsenal, including missiles capable of striking the US mainland.