Assistant Secretary at the Department of the Taoiseach, Liz Canavan, said that a growing number of cases had been identified in clusters, but some close contacts are not being tested.
"Public health doctors are reporting a growing number of clusters around the country in recent days.
"But they're also reporting a growing proportion of people identified as close contacts of possible cases who, when offered a test are not coming forward," she said.
"Testing is a foundation stone of everything we're doing in this.
"If we don't know how many people have it, if we don't know where the disease is, we can't stop it spreading.
"So, please, if you're asked to get a test, do so."
Ms Canavan said that the government was aware of the disappointment of pubs over the pausing of re-opening of the economy, but said that the rate of infections had "crept up".
She said that people must be reminded that Covid-19 is "highly infectious and spreads fast".
The R number being 1.8 means that "the disease starts to take hold again", she said.
It is more important to avoid going backwards in the roadmap than continue re-opening, Ms Canavan said.
"You may be wondering why did this happen? Did we move too soon?
"The reality is that more people are moving around than they were a number of weeks ago.
"That creates better conditions for the virus. The government has assessed a balance of risks and will continue to do so.
"So, for now, the public health measures will remain in place until August 10."
Ms Canavan urged people to avoid crowded places, saying that "if a place feels unsafe, it probably is unsafe".
Ms Canavan added that 67,400 employers are now registered for the Temporary Wage Subsidy Scheme, with around 405,000 employees having been paid a total of €2bn since the outbreak began.
A further 345,600 are on the Pandemic Unemployment Payment, down 67,300 from last week - the largest week-on-week reduction in the figure.
At its peak, 598,000 people were on the payment.