An international team of investigators are due to release a report on the sinking this week. The South has intimated that blame for it lies with the North, although it has not officially said so.
As for Saturday's incident, the patrol boats were said to have violated the Northern Limit Line (NLL) border.
One North Korean ship broke the border and returned after receiving a radio warning from the South, the officials said.
A second boat from the North entered the waters about 50 minutes later and ignored a radio warning before the shots were fired.
"The North's patrol boats did not respond and returned north. There were no casualties," the South's spokesman said.
Naval battles between the countries occurred in the same region in 1999 and 2002, and, in November 2009, a firefight led to a North Korean boat being set ablaze.
The North does not recognise the NNL border, which was set by the US-led UN Command after Korean war from 1950 to 1953.