Pakistani fighter jets pounded Taliban positions in a district near the Swat Valley on Tuesday as ground troops pressed on, in the military's most robust effort to repel a Taliban advance.

Pakistan faces intense pressure from Washington to abandon a peace deal with the Taliban in Swat, which has become a major militant base since the deal was struck in mid-February. Tuesday's fighting in the neighboring Buner district seemed likely to further undermine the already shaky accord.

The...