The letters may have raised tensions, but they didn't produce the all-out street war the KGB was hoping for, probably because '70s America was not in fact run by those costumed gangs from The Warriors. So the frustrated Soviets decided that if no one was buying their fake racist attacks, they would have to carry out a real racist attack. After all, if you want racism done right, you have to do it yourself.
In 1971, high-ranking KGB officer Anatoli Kireyev ordered agents to plant a bomb in "the Negro section of New York." After the bomb went off, the agents were supposed to make anonymous phone calls claiming JDL responsibility. Fortunately the plan didn't happen, although the reasons for this are unclear (accessible KGB archive material only contains the orders from Kireyev, not any responses). Given that this was the summer of 1971, maybe nervous KGB agents had just seen Shaft and didn't want to risk it.