Ministry spokesperson Kim Eui-do urged Pyongyang to back up its words with real work and show its sincerity, Xinhua reported.
South Korea received a notification from Democratic People's Republic of Korea's (DPRK) peace panel which asked if the reunions could be held in peace due to South Korea's "war drills" and planned joint military exercises, the Yonhap news agency reported.
It also said: "If there is no other thing happening in the south side and if it has intent to discuss the proposals of our side, both sides can sit together in a good season and discuss the matter."
South Korea said Pyongyang's demands might refer to its repeated calls for talks aimed at resuming a tour programme to Mount Kumgang, North Korea's scenic mountain resort.
The spokesperson said the South Korean government has been insisting on dealing with family reunion issues and resuming a tour programme to Mount Kumgang separately.
The two sides agreed to hold family reunions at Mount Kumgang last year but Pyongyang abruptly cancelled the agreement at the last minute.
The tour, launched in 1998, was halted in July 2008 when a South Korean woman tourist was shot dead by a DPRK solider for venturing into an off-limit area.
The DPRK has since repeatedly called for resuming the tour programme.
But South Korea said that the tour could be resumed only when causes and liability for the suspension are made clear and responsible measures are taken to prevent another incident.
South Korea's unification ministry Monday offered to hold a working-level meeting over the issue.
--IANS (Posted on 09-01-2014)