Kopecky, the 2010 champion, had won the previous two stages in Spain, narrowing the gap on overall leader Mikkelsen.
But in SS6 the Norwegian was 3.5 seconds quicker than fellow SKODA Fabia driver Kopecky and now lies 5.1s ahead of the Czech with three stages of day two remaining.
"It was a good stage for us, a good push throughout the stage," said Norwegian Mikkelsen. "I had a very good rhythm with no mistakes, a good feeling. Jan is very quick at the moment so we need to push quite hard to stay in front."
Luis Monzon was the top Peugeot driver with the third fastest time, 1.4s quicker than Hermann Gassner Jr.
Stage seven, Ingenio 1, gets underway at 17:29 local time (16.29 UK time).
Earlier, Kopecky won stage five ahead of Mikkelsen, the Czech’s second consecutive victory of the rally.
"The last two kilometres were difficult because the car was sliding a lot on the tyres because it’s a lot warmer now," said Kopecky, who was 0.5s quicker than Mikkelsen.
Monzon was third in his Peugeot 207 S2000 with Gassner Jr fourth.
Kopecky’s stage four win had ended Mikkelsen’s dominant run on day one of the rally.
1. Andreas Mikkelsen (SKODA Fabia) 00:56:33.6
2. Jan Kopecky (SKODA Fabia) 00:56:38.7
3. Luis Monzon (Peugeot 207) 00:57:38.0
4. Hermann Gassner Jr (SKODA Fabia) 00:57:46.0
5. Sepp Wiegand (SKODA Fabia) 00:58:03.6
6. Alberto Hevia (SKODA Fabia) 00:58:05.9
7. Jonathan Perez (Peugeot 207) 00:58:59.7
8. Oleksii Tamrazov (Ford Fiesta S2000) 00:59:54.8
9. Joan Vinyes (Suzuki Swift S1600) 00:59:56.0
10. Gorka Antxustegi (Suzuki Swift S1600) 01:00:11.3