The vote, in 35 of Nigeria's 36 states, should give foreign monitors further evidence of how fair presidential elections next month will be.
The opposition won because thanks to the thousands of foreign monitors, the voters knew their votes were secret.
The organization's 1,300 foreign monitors may evacuate on Sunday if peace talks fail.
The report says that in Pristina, the situation changed considerably once foreign monitors left.
The heavy troop presence could easily block the departure from Kosovo of foreign monitors, one observer said.
The other foreign monitors were even more enthusiastic.
But foreign monitors said some practices followed on Saturday needed to be improved for the presidential elections.
Every day, the foreign monitors who patrol Kosovo say, small fires have to be stamped out to prevent renewed combat.
While not free from irregularities, the results were generally accepted as accurate by foreign and domestic monitors.
"On paper our program is working well," a senior foreign military monitor said.