Tectonic tremors have been detected in New Zealand, including the Gisborne and Manawatu regions in the North Island and along the Alpine Fault in the South Island. Here we report a regional analysis of tremor activity in New Zealand and present a potential relationship between slow and ordinary earthquakes. We first construct a tremor catalog in the Cape Turnagain, Marlborough, and Puysegur regions that spans the 2005–2016 time period using the GeoNet permanent seismometer network, and extend the tremor catalog in Manawatu to cover the same period. We employ an envelope cross-correlation method to detect and locate the seismic events, then extract the tremor-like events using a scaling-law-based criterion that is a function of the event duration and seismic energy, and finally select the tremors by visual inspection. We find that the tremors in Cape Turnagain temporally coincide with known shallow slow slip events in the region. We are also able to relate the increased tremor rates during 2010–2011 and 2014–2015 to two deep slow slip events in Manawatu. However, known slow slip events cannot explain all the increases in the tremor rate throughout Manawatu. Tremors in the South Island occur near recent large earthquakes, such as the 2016 Mw 7.8 Kaikoura Earthquake in Marlborough and 2009 Mw 7.6 Dusky Sound Earthquake in Puysegur, suggesting a possible relationship between slow and fast tectonic processes.