Plans to restart screening services are being finalised, with the phased restart due by the end of the summer.
Assistant general secretary at the Department of the Taoiseach Liz Canavan said that the restart of the services was "a priority" but that it had to be done safely.
Screening services were cancelled in March when the Covid-19 pandemic began, with experts saying that programmes which involved intimate examinations could not continue during the public health emergency because of the need for social distancing.
However, with more businesses opening, questions have been raised from both politicians and the public about the resumption of testing.
Ms Canavan said that people who were to be screened would receive invitations.
"The HSE is finalising plans to reestablish non-Covid health supports and services and expects to provide a further update in the coming days.
"The safe restart of screening is also a priority for the National Screening Service. The four screening programs are now finalising the plans for a phased reintroduction of screening.
Screening restart plans are currently being aligned with the wider health care system, and screening restart dates are expected to be announced by the end of June.
"We're expecting to begin a phased reintroduction of the national screening service programs by the end of the summer and screening invitations will be issued on a phased basis, according to clinical prioritisation."
Ms Canavan also said that over 125,000 people have returned to work having been on the Pandemic Unemployment Payment since Covid-19 restrictions began to be eased.
"Today, approximately 465,900 people who were unemployed last week will receive a weekly payment of €350 under the COVID-19 pandemic unemployment payment scheme.
"This is a reduction of 32,800 on the number of people paid last week. The overall value of the weekly payment is in the region of €163 million.
"Last week, approximately 23,900 people in receipt of pandemic unemployment payment closed their claim as they had returned to work. Since the start of reopening over 125,000 people have closed their claim, as they have returned to work."
Ms Canavan also said that 61,800 employers were now being supported by the Temporary Wage Subsidy Scheme, with 410,000 employees having received some €1.6 billion.