We report the detection of off-pulse emission from two long-period pulsars PSR B0525+21 and PSR B2045-16 using the Giant Metrewave Radio Telescope. We recorded high time resolution interferometric data at 325 MHz and gated the data off-line to separate the on- and off-pulse sections of the pulsar. On imaging the two temporal sections separately, we detected a point source in the off-pulse images of both the pulsars coincident with the pulsar locations in the on-pulse images. The long periods (3.75 and 1.96 s, respectively) and low spin-down energies (erg/s) of the two pulsars argue against a pulsar wind nebula (PWN) origin for the off-pulse emission. The derived estimates of the interstellar medium particle density required to drive a PWN do not support such an interpretation. A magnetospheric origin for the off-pulse emission raises questions regarding the location of the emission region, which is an important input into pulsar emission models.