Almost 50,000 students had already received first-round offers, with 37,645 accepting the initial offer.
The unprecedented uptake in initial offers has seen only 3,236 students receiving secondary offers.
It is common practice for third institutions to make more offers than they expect to fill. The actual number of vacancies is thought to be as low as 1,000.
Competition for places in science and engineering courses is particularly intense, with almost 85% of places now filled.
Demand in these areas has grown as they are perceived to offer greater prospects of employment in the current economic climate.
While most science places were filled following the first round offers, limited places do remain. Trinity is making offers for place in it prestigious science programme, with points reducing from 510 to 500.
In contrast, interest in Arts courses have shown a marked reduction; the points for Arts at UCD have been reduced by 5 points with places still available
In total 17,286 applicants remain without an offer, a reduction of 700 on last year.
Students, who have yet to receive a satisfactory offer, can still apply for any remaining vacant course places in the coming week.