Mr Anderson said that while the Rena appeared to remain stable on the reef, the situation could change with more bad weather.
"How much weather, I don't know. I've said the word precarious, and it is. We need to monitor it at all times."
A false report by TVNZ on Tuesday night that the Rena was breaking up had sparked a "flurry" of phone calls and left crew members and those on board the on-site bunker barge Awanuia "bemused", he said.
"The Awanuia master was sitting watching it and saw no movement ... and he was absolutely laughing down the phone."
Meanwhile, a "weak front" due to arrive over the Bay of Plenty today was expected to bring light winds and the chance of slightly larger swells and it was not until next Wednesday that a new front would arrive, said MetService weather ambassador Bob McDavitt.
"It's not too frightful - we've got our fingers crossed."
Weatherwatch.co.nz analyst Philip Duncan said the new front was expected to herald a week of strong nor'westers - but without the swells that wrecked the ship a week after it ran aground.
"It doesn't look too severe at all. I don't see anything too dramatic, or certainly nothing as big as they had in the first week," Mr Duncan said. "We're in the middle of spring and it's so settled ... It could be a lot worse."
The weather window came at a time when salvors were moving into a crucial part of the pumping operation.
By the time salvors stopped yesterday to reposition the pump, about 772 tonnes had been removed from the Rena.
Their efforts had nearly emptied the port-side number 5 tank, with just 35 tonnes remaining as salvors lifted a 100kg pump through it.
Their next job is to off-load the 25 tonnes in the engine room settling tanks.
Dive teams have been building a cofferdam within the Rena to allow access to the submerged starboard number 5 tank.
Around 200 volunteers are expected to hit Mount Maunganui's main beach and Papamoa today to clean up the oil spill from Rena.
National On Scene Commander Nick Quinn says fresh light oiling around Mount Maunganui and Leisure Island has been identified.
He says their focus for the next couple of days will be to get clean-up crews there cleaning that oil.
Beaches east of Tay Street to Maketu Spit remain closed.
Mr Quinn says with the current levels of oil still in the environment it's unlikely they'll open in time for the weekend.