The Department of Health in the region said the rate rose from between 0.5 to 1 last week, to between 0.8 and 1.8 this week.
'R' represents the number of individuals who, on average, will be infected by a person with the virus. A measure above one is an indication that infections are on the rise.
The news comes as more than 20 new coronavirus clusters have been identified in the North.
Of the 23 pinpointed in the region since May 25th when the test and trace programme went live, 11 clusters remain open, according to the North's Public Health Agency (PHA).
Some 168 cases of Covid-19 have been associated with these clusters, with nine of the clusters having had five or more cases associated with them.
Earlier this week, two businesses in Newcastle, Co Down, closed temporarily following outbreaks among their staff.
The statement from the PHA came on Thursday as the Department of Health’s daily updates showed that 43 more positive cases of coronavirus have been detected in the region, bringing the total to 6,049.
No new deaths were recorded on Thursday, leaving the total in the region at 556, according to departmental figures.
The PHA has defined a cluster as two or more laboratory-confirmed cases of Covid-19 among individuals associated with a key setting, with illness onset dates within a 14-day period.
Key settings which have seen a cluster include workplaces, retail or hospitality premises, domestic gatherings, and sporting settings, however the PHA said the transmission risk is highest in a household setting.
Since July, the average number of close contacts linked to cases has more than doubled. The rise may be attributed to the gradual easing of lockdown measures, but may also be explained by relaxing of attitudes to social distancing.
Dr Gerry Waldron, head of health protection at the PHA, said: “Clusters are managed through the contact tracing programme, and where we need to advise or inform the public of any increased risk to public health we will do so in a timely manner.
“In the past seven days, five clusters have been identified. Thirty-five cases have been associated with these clusters, with 239 close contacts.
“This should act as a timely reminder that we must not become complacent – coronavirus remains in circulation and we have seen an increase in cases in recent weeks. It is therefore essential that we remember the key advice to help keep ourselves and those around us safe.
“Maintain social distancing, wash your hands regularly, and get tested if you display any symptoms of coronavirus.”
Dr Waldron added: “Speculation around current clusters of Covid-19 across Northern Ireland is not helpful.
“We will not be commenting on individual cases of Covid-19 or going into the detail of every incident that emerges, as this could lead to people being identified, create stigma, and focus attention on individuals, families or groups, and therefore deter others with symptoms coming forward to be tested.”
