A total of 13 containers were removed on Saturday and 15 on Friday, meaning a total of 195 containers have so far been removed from the wreck, said MNZ.
Salvors will today focus on installing patches in the corridors of the wreck to improve buoyancy, said MNZ.
Today's forecast is for continuing showers and patchy rain with light bursts of wind. More of the same drizzly rain is forecast for Tuesday and Wednesday.
An overhead flight of Rena this morning showed a visible metallic sheen of oil about 4.5km long from the vessel, MNZ said.
A beach cleaning team is working today at Shark Alley and Leisure Island to remove small amounts of oil sighted in the area, and teams are continuing work on the north and western sides of Motiti Island and Maketu Spit.
Clean up teams are also working at Kulim and Fergusson Parks and Matakana Island, while warm water rock washing continues at Mauao.
A total of 967 tonnes of solid waste had been collected so far, MNZ said.