Work has also started on bringing down NZI House and the Westpac building, while the owners of the Holiday Inn are managing the demolition of their own building.
In the next fortnight, Cera will finalise contracts for the PricewaterhouseCoopers building, Mr Brownlee said.
"As the more significant demolitions progress, it will make it easier to reduce the cordon," he said.
"We had said that we'd like that cordon down completely to perhaps just being around some buildings by April but as more assessment has been made ... that has become less and less possible.
"But every effort is being made to reduce that cordon as quickly as possible, starting with the eastern side coming back into the city.
"There's so much to be done. You can't mix up a demolition site with a construction site."
While the government has failed to meet its self-imposed deadline on lifting the cordon, Mr Brownlee did highlight good news for the local economy.
He pointed to "extraordinary economic figures" for Canterbury over the final quarter of last year, with strong showing from the manufacturing sector and "record" freight movements through the port and airport.
National Bank Regional Trends Economic Survey for the months to December, showed that Canterbury had economic growth of just under one per cent, which compared "very favourably to the rest of New Zealand", the minister said.
He also highlighted the latest unemployment rate dropping from 5.2 per cent to five per cent - compared to the national average of 6.3 per cent - while job advertisements had jumped by "about five per cent."
Brownlee said: "After the earthquakes there were suggestions we could lose large chunks of the population and the economy here would almost completely disintegrate, making the place a bit of a basket case. Nothing could be further from the truth.
"It's a great tribute to people here in Canterbury who've made efforts in their daily lives to keep businesses open, to keep their work places providing services, right through from social services to retail shopping, and that tribute is seen with the extraordinary economic figures that are coming out of Canterbury.
"It shows that Canterbury is making progress and we're just starting to see the thin end of what will be a sharp wedge upward in our rebuilding activity.
Cera chief executive Roger Sutton also welcomed the figures. He said: "The city is going flat out, and all those economic indicators remain very positive.