Nowadays, the generation of laser pulses focused to a spot size comparable to the wavelength and whose duration is only a few optical cycles of the electric field is achievable. Moreover, TM01 laser pulses are of considerable interest, among other things, because of their remarkable focusing properties. In order to describe theoretically the spatiotemporal behaviour of such nonparaxial, ultrashort TM01 pulses, one needs expressions of their electromagnetic fields. To obtain these expressions, Maxwell's equations must be solved rigorously. The method of the Hertz potential, the complex-source/sink model, and the use of a Poisson-like spectrum are exploited to solve the vectorial wave equation. Closed-form expressions for the electric and the magnetic fields of an isodiffracting TM01 pulse are presented and they can be used to study the behaviour of tightly focused, ultrafast TM pulses.