"A joint committee formed by the two countries... has recently held its first meeting in Riyadh," the KUNA news agency quoted Ali al-Omair as saying late Tuesday.
The dispute has seen the closure of the Khafji and Wafra oil fields in the neutral zone, which have been pumping for more than half a century.
The two fields together produced more than 500,000 barrels per day which was equally shared between the two countries.
Omair said there was no timeframe for the talks but that he expected a breakthrough shortly.
The offshore Khafji filed was shut down by the Saudi side in October over environmental issues.
Wafra was closed in May for a two-week maintenance and did not resume production.
Industry sources say Kuwaiti authorities were unhappy with Saudi Arabia for renewing an operating agreement for the Wafra field with Saudi Arabian Chevron for 30 years in 2009 without consulting them.
In response, it stopped issuing or renewing visas for Chevron foreign employees.
The halt to output comes amid a worldwide supply glut that has driven down prices of crude.
The dispute has been a blow particularly to Kuwait which, unlike its much larger neighbour, has little spare output capacity to compensate for drops in production.