Mr Kerry landed in South Korea on the first leg of an Asian tour that will also take in Beijing and Jakarta.
He is expected to meet President Park Geun-hye and be briefed on the inter-Korean talks.
An official in Seoul said Wednesday’s talks had failed to narrow differences between North and South Korea.
The Unification Ministry official, quoted by South Korea’s Yonhap news agency, said North Korea had asked Seoul to delay joint military exercises with the US set for later this month.
Seoul had rejected the request, the official said, and said forthcoming family reunions should not be linked to the drills.
“We proposed that South and North Korea build confidence by implementing the family reunions,” the official said
The family reunions – which bring together relatives divided by the partitioning of the Korean peninsula in 1953 – will be the first since 2010.
They are due to begin on 20 February, four days before the annual US-South Korea joint military exercises begin.
North Korea describes these exercises as preparations for war and has issued multiple calls for them to be cancelled.
On Thursday, South Korea said plans for the drills had been in place for months and the exercises would go ahead.
“It is wrong to relate the defensive nature of (a) military drill (which is) for national security to the separated family reunion which has a humanitarian objective,” said Defence Ministry spokesman Kim Min-seok.
Last year’s drills, which followed North Korea’s third nuclear test on 12 February, were followed by a prolonged period of tension and extreme rhetoric from North Korea, including threats of attacks.
The two Koreas did agree to hold further talks, but set no date for a meeting, the Unification Ministry said.
Mr Kerry will spend a day in Seoul before flying to Beijing on Friday morning.
As well as North Korea, he is also expected to raise the issue of South Korea-Japan ties. Rows over historical and territorial issues have left relations between America’s two main allies in the region strained.