Around 50,000 people have received a first dose of coronavirus vaccine in Northern Ireland, Health Minister Robin Swann said.
Nine in 10 care home residents have been inoculated.
By January 18, more supplies are expected to be received from manufacturer AstraZeneca.
Mr Swann urged the public to stay at home while the programme gathers steam.
“This is a time to hunker down and weather the crisis,” he said.
Lockdown measures were introduced immediately after Christmas to stem the rising tide of infections, including the closure of non-essential retail and hospitality.
The minister said: “We have already seen a decline in cases, albeit over the last couple of days, which ties in with the two-week lag (in measures affecting the figures).”
He said there had been a “substantial” increase in the virus’ transmission in recent times.
The minister warned infection figures need to be driven down before an expected peak in hospital admissions during the latter part of this month.
He said: “Lockdown will be vital in that.”
He declared there were real grounds for optimism for the future.
Two vaccines have been approved and are being distributed in Northern Ireland.
Doctors at GP surgeries began vaccinating the over-80s earlier this week.
Mr Swann told the Assembly that 30,000 healthcare staff have received the jab.
Some 504 boxes of AstraZeneca, representing 50,400 doses, have been received.
So far, 45 GP practices have been given the vaccine to administer to their staff and the over-80s.
From the start of the next week, all practices will have received 100 doses, the minister said.
The SDLP’s Cara Hunter asked if the department was considering using vaccination vans, door-to door-vaccinations, drive-through vaccination sites, 24-hour options or the re-purposing of Covid-19 testing sites.
Mr Swann said they could not divert their testing centres.
He added: “We need them more than ever now.”