In April, the Central Bank gave lenders six months to curtail lending to governments and their commercial holding companies .
The deadline to implement the rules passed 10 days ago, but several banks admit they are in breach.
On Monday, National Bank of Abu Dhabi's chief executive, Michael Tomalin, said the bank had secured a six-month extension to the September 30 deadline to apply the new regulations.
But Mr Al Qemzi said even an extra six months might not be enough time.
"It's logistically difficult" to comply with the rules, he said. "I think time is required. Time is very important, whatever you want to do. We're just getting out of the crisis, and we're watching levels of liquidity heading up. Six months isn't enough … things like this need three years, at least."
He added that Noor Islamic Bank was also in breach of "some" of the Central Bank limits, mainly because of its exposure to Dubai Group.
The lender has received no guidance from the Central Bank on how to comply, Mr Al Qemzi added.
Noor Islamic Bank's ownership is split between a 5 per cent stake held by the Emirates Investment Authority and a 95 per cent stake held by Noor Investment Group.
The group is a holding company jointly owned by Dubai Holding, Investment Corporation of Dubai, and UAE businessmen. Dubai Holding is the parent company of Dubai Group.
It is unclear whether the extension to the Central Bank's deadline affects all lenders, although other banks say they have not been advised by the Central Bank on how to apply the new lending limits.
The Central Bank did not respond to repeated requests for comment. On October 3, a spokesman said that there would be no extension to the lending limits.
With few communications from the Central Bank since then and the debate becoming increasingly divided, two Dubai banks last week privately floated the idea of a "mop-up fund" operated by the Central Bank or another federal body to buy up lenders' government exposures.
Analysts say that idea is unlikely to be implemented and would effectively be a capital injection.
Banks say they are unable to sell their exposures because many European banks are already selling assets in an effort to shore up their own capital bases.
The Emirates Banks Association, which is leading negotiations with the Central Bank on behalf of the banking industry, declined to comment on the discussions.
Representatives of Emirates NBD, which has said it is in breach of the Central Bank limits, were unable to comment.