Is every long exact sequence $$\cdots\to\pi_{d+1}(B)\to\pi_d(F)\to\pi_d(E)\to\pi_d(B)\to\pi_{d-1}(F)\to\cdots$$ induced by a Serre fibration $p:E\to B$ ?

If not, what are the conditions under which this is the case?

Thank you!