We demonstrate quasi-continuous tuning of the emission frequency from coupled cavity terahertz frequency quantum cascade lasers. Such coupled cavity lasers comprise a lasing cavity and a tuning cavity which are optically coupled through a narrow air slit and are operated above and below the lasing threshold current, respectively. The emission frequency of these devices is determined by the Vernier resonance of longitudinal modes in the lasing and the tuning cavities, and can be tuned by applying an index perturbation in the tuning cavity. The spectral coverage of the coupled cavity devices have been increased by reducing the repetition frequency of the Vernier resonance and increasing the ratio of the free spectral ranges of the two cavities. A continuous tuning of the coupled cavity modes has been realized through an index perturbation of the lasing cavity itself by using wide electrical heating pulses at the tuning cavity and exploiting thermal conduction through the monolithic substrate. Single mode emission and discrete frequency tuning over a bandwidth of 100 GHz and a quasi-continuous frequency coverage of 7 GHz at 2.25 THz is demonstrated. An improvement in the side mode suppression and a continuous spectral coverage of 3 GHz is achieved without any degradation of output power by integrating a π-phase shifted photonic lattice in the laser cavity.