Multipath propagation may result in ISI because of the delay spread. In general, the time delays of different paths are different. That is, the signals from some paths arrive at the receiver earlier, but from some paths arrive at late. When these signals from different paths arrive at the receiver, different symbols are overlapped together and ISI occurs. From another point of view, when a narrow pulse passes through a such kind multipath channel, the output is a wider dispersive pulse.
On the other hand, if all paths have a same delay, and all signals from different paths arrive at the receiver at the same time, then the delay spread is zero, and no ISI occurs.
I agree with the previous answer but let me encourage more precise language. Inter symbol interference (ISI) is caused by multipath propagation where delayed parts of a symbol arrive at the same time as parts of another symbol from a different path causing ISI. Fading is another issue caused by multipath propagation, if two or more propagation paths occur (within a symbol or not) they can combine destructively because of different carrier phase on the paths causing fading. The core problem is multipath propagation which causes ISI and fading.