Doctors have insisted there is no postcode lottery when it comes to rolling out the coronavirus vaccines.
Northern Ireland's vaccination plan means all those over 80 should receive their first dose by the end of January.
More than 154,000 doses of a vaccine have now been administered, health officials said.
Dr Frances O'Hagan, deputy chairwoman of NI's GP committee, said practices had their own rollout plans but she expected them to meet official targets.
"As soon as we get the vaccine, we will get it to you," she told BBC News NI. "But please, please wait until we contact you."
"We tailor our programmes to our individual patients and to our geography and to our surroundings.
"It's not actually a postcode lottery. It's the best way of doing it because we know what suits our patients."
Dr O'Hagan said she had not heard reports of some practices holding back vaccines until they received bigger amounts to allow for a larger number of vaccinations to be done.
She said rolling out the programme was a logistical challenge which fell on top of an already heavy workload but the jab would be given out in a "safe and timely" fashion.
Sinn Féin MP Órfhlaith Begley said doctors in her West Tyrone constituency were working above and beyond to administer the vaccine to as many people as possible.
"But unfortunately I am hearing that some GPs cannot access supplies of the vaccine," she said.
"There does appear to be, and it is a consistent message from GPs in my own constituency, a feeling the distribution of the vaccine has been unequal to date."
Meanwhile, Health Minister Robin Swann has welcomed a further delivery of the Oxford-AstraZeneca vaccine into Northern Ireland on Tuesday morning.
In a tweet, Robin Swann said: "We now have the supply to complete all our over 80s and when that group is finished, there will be enough to start into the over 75 programme."
Patricia Donnelly, the head of NI's vaccination programme said there had been 154,436 doses of the vaccine administered here, with 132,857 of those being first doses.
On Tuesday, she said three quarters of care home residents had already received both doses.
"With the arrival of additional vaccine today, which have been issued this afternoon and tomorrow to GPs, there will be enough to complete the over 80 population and to commence in the over 70 population," she added.
A further 24 virus-related deaths and 713 more Covid-19 cases were reported in Northern Ireland on Tuesday.
It brings the total number of deaths recorded by the Department of Health to 1,649.
There are currently 842 people in hospital with the virus, 70 people in intensive care units (ICU) and 57 being ventilated.
In the Republic of Ireland, a further 93 Covid-19 related deaths were reported on Tuesday, bringing the country's death toll to 2,708.
A further 2,001 positive cases were also recorded in the latest figures from the Republic's Department of Health.
Northern Ireland's rate of Covid-19 infection is now below one and has been at that level for a couple of weeks, according to the chief medical officer.
However, Dr Michael McBride warned the reproduction (R) number for hospital transmission remains above one.
Dr McBride said new variants of the virus had made the job of curtailing the spread even more difficult, and warned he did not foresee any relaxation of restrictions any time soon.
"We need to ensure that we have as many people who remain at risk of severe disease vaccinated and prioritised with the first dose as possible before we consider significant relaxations in the current restrictions," he said.
Meanwhile concerns have been raised that "social media myths" are encouraging some care home staff to reject the Covid vaccine.
Pauline Shepherd, from the Independent Health and Care Providers, said young women were especially vulnerable to misinformation about the vaccine and fertility.
Last week, the Department of Health said there had been an uptake level of about 80% among care home staff.
"We are very keen obviously that everyone takes the vaccine, that is really the only way that we are going to get through this," she told BBC Radio Foyle.
"Obviously there are myths going around on social media about the vaccine and some are opting not to take it.
"Particularly younger females seem to have the view through social media that it may impact fertility".
There are currently 139 confirmed Covid-19 outbreaks in NI's 483 care homes.
The Public Health Agency (PHA) and Department of Health were now exploring how "to dispel the myths", Ms Shepherd added.
Dr Mukesh Chugh, a consultant anaesthetist at Altnagelvin Hospital in Londonderry, said there had been a "reluctance" among black, Asian and minority ethnic (BAME) people to take Covid-19 vaccines.
Dr Chugh says this is because of "anti-vaccine messages" posted across various social media platforms and messenger apps "targeted at certain ethnic and religious groups".
"I encourage them not to believe the messages they are getting on WhatsApp - these are not scientific messages," he said.
"Believe the scientific research."
Meat plant workers
On Tuesday, Agriculture Minister Edwin Poots said a number of groups of key workers should be given priority access to vaccinations.
Prioritisation was decided by the Joint Committee on Vaccination and Immunisation (JCVI), which advises UK health departments on immunisation.
Asked if he supported prioritisation for food workers in meat plants, Mr Poots told the assembly he did and had raised it with the executive.
"It's been identified as an essential service - those people working in them are there in cold, wet conditions where we have had a number of outbreaks," he said.
"We should seek to introduce those people somewhat earlier than is currently the case - I will continue to endeavour to press that case."
He said other groups of workers who should be prioritised included "teachers and police officers".