This was after the sector's main trade union said it would launch a strike at the world's top three producers this week.
Members of the Association of Mineworkers and Construction Union (AMCU) voted overwhelmingly on Sunday to strike at the world's biggest producer, Anglo American Platinum.
That followed recent votes to strike at Impala Platinum and Lonmin Plc. A simultaneous stoppage at the three would hit an important export at a time when the rand currency is near a five-year low, and further dent investor confidence in Africa's largest economy.
"The platinum industry needs to seriously get around the table," Gordhan told state broadcaster SAFM in an interview.
"We can least afford another round of strikes that will act as a destabilisation to the platinum sector which has had increasing difficulties over the last 18 months."
Renewed labour unrest would also be an unwelcome distraction for President Jacob Zuma and his ruling African National Congress ahead of general elections expected in three months.
At Anglo American Platinum and Lonmin, the union is seeking a minimum monthly wage of 12,500 rand ($1,200) for entry-level workers - more than double current levels, under the populist banner of a "living wage".
At Impala, the union scaled back its demand late last year to just over 8,500 rand a month.
Companies have said they can ill afford steep increases as power and other costs soar while prices for the white metal used in emissions-capping catalytic converters in automobiles remain depressed.
Platinum's spot price shed 11 percent last year and is about 40 percent down from record peaks scaled in 2008.