Engen fuel stations in Gauteng are running dry because oil tankers are unable to leave some depots, Engen Refinery said on Wednesday.
"Gauteng is the hotspot. Three of the depots can't release oil tankers because truck drivers are on strike, and there has been a bit of intimidation," said spokesperson Tania Landsberg.
"There are people picketing outside the gates of the depots and the most important aspect for us is ensuring the safety of our workers."
The depots affected were Langlaagte, Alrode, and Waltloo.
Landsberg said although contingency plans were in place there would be challenges.
"We are planning around that to keep our sites wet, but some [have] already gone dry."
The refinery had not yet been updated about fuel shortages in the coastal areas.
Shell South Africa Refining spokesperson Dennis Matsane, and BP Southern Africa spokesperson Glenda Zvenyika were not immediately available for an update.
On Tuesday, Zvenyika said fuel deliveries were increased before the strike to ensure all its petrol stations were topped up.
The Chemical, Energy, Paper, Printing, Wood, and Allied Workers Union (Ceppwawu) rejected the intimidation claims by Engen.
"They want to discredit our strike and want to run away from the fact that the strike has had an impact on employers and they want to underplay that," said union coordinator John Appolis.
"Our members are on strike and that is why they can't deliver fuel. It's not because of intimidation."
He said the strike by fuel workers had been peaceful.
"Instead of making wild accusations, the employers must make a decent wage offer so that this dispute can end."
Since workers handed over a memorandum to employers on Tuesday, there had been no response, said Appolis.
The Fuel Retailer 'Association said most service stations were receiving fuel deliveries despite the countrywide strike.
Sasol spokeswoman Nothemba Noruwana said contingency plans were in place, and that major complexes in Secunda and Sasolburg were operating with minimal disruptions.
About 70 000 fuel workers from Ceppwawu, the Allied Workers Union, and the General Industries Workers Union of SA downed tools on Monday, demanding a minimum salary of R6 000 a month and a 40-hour working week.