Mansoor claimed the success in Kunduz countered Afghan government pronouncements "that the people of Afghanistan are against the Taliban and want to rid them from their country."
The word claimed is being used like the word said. Writers often like to use the word claim like this when they don't agree with what someone else is saying. We can understand the sentence like this:
- Mansoor said that [the success in Kunduz countered Afghan government pronouncements "that the people of Afghanistan are against the Taliban and want to rid them from their country"].
That bit in brackets, [], is a content clause. It tells us the content of what Mansoor said. Here is the clause on its own:
- The success in Kunduz countered Afghan government pronouncements "that the people of Afghanistan are against the Taliban and want to rid them from their country".
Here the Subject is the success in Kunduz. This refers to the Taliban's success in capturing the city of Kunduz. Mansoor says that the Afghan government believe that the Taliban is unpopular in Afghanistan. The government says that the Afghan people do not want the Taliban in their country.
However Mansoor, who is a Taliban leader, said that it was very easy for the Taliban to take over Kunduz. It took them a few hours and only a few hundred soldiers. There were thousands of Afghan Army soldiers there, but the Taliban were still able to take control of the city.
Mansoor's argument is that if the Afghan people didn't want the Taliban they would have fought to keep them out. It would not have been so easy to take the Kunduz. Mansoor is implying that the fact it was easy to take the city shows that the Afghan people want the Taliban.
So "the success in Kunduz" counters the Afghan government's argument.
Footnote
Of course, this is just what Mansoor said. The Afghan government troops had retaken the city within a few days.