About 50% of those aged 18 and over and two-thirds of 30 to 40-year-olds have had a first dose.
About 95% of all those aged over 50 have had a first dose of a Covid-19 vaccine.
Overall, about 60% of adults in Northern Ireland are fully vaccinated with two doses.
Bernie Owens, from Belfast Trust, said: "We are coming to the end of the vaccination programme, we are so close.
"So we are trying to do this final push to get the 18 to 29-year-olds, and the 30 to 40-year-olds who've been later being offered the vaccination appointments, to come forward now and we're trying to make it as accessible for them as is possible," the senior director continued.
In Belfast, a walk-in unit operated in the grounds of City Hall until 20:00 BST, offering Pfizer to anyone unvaccinated aged over-18.
Drop-in clinics were also open in parts of County Down, including at the Quays shopping centre in Newry.
In Castlewellan on Saturday and Newcastle on Sunday, vaccine 'buses' will be offering Moderna vaccines.
* Castlewellan Community Centre 11:00-19:00
* Belfast City Hall 14:30-20:00
* The Quays, Newry 09:30-15:30
* Newcastle Community Services, Newcastle 11:00-19:00
Doses of the Pfizer jab will be administered in Newry and Belfast, Moderna will be issued in Castlewellan and Newcastle.
No appointment is needed, however those attending must bring photo ID.
District nurse Suzanne Rogan, who will be on board to administer the vaccines, said people need to bring photographic ID and, where possible, their health and social care number.
"They will be in and out within minutes," she added.
Walk-in slots for second doses are also being offered at the South Eastern Vaccination Centre at the SSE Arena in Belfast.
Anyone who has had a Pfizer vaccine six weeks ago or an AstraZeneca vaccine eight weeks ago is eligible. Second doses cannot be administered at a shorter time interval.
'Potential for another wave'
There has been a sharp rise in the number of positive Covid cases in Northern Ireland compared to a week ago.
However, the number of hospitalisations has not increased significantly: more than 20 patients are currently being treated for the virus, and there is one person on ventilation in an intensive care unit.
Health officials are also investigating large social gatherings involving young people, as Stormont's chief scientific adviser Prof Ian Young warned of the potential for another Covid wave.
Earlier this week, executive ministers were told that the highly transmissible Delta variant, first detected in India, now accounts for 75% of Covid infections and that there has been a slight increase in the R number (the rate of transmission) from between 1.2 and 1.5 to between 1.2 and 1.6.