The HSE says over two-thirds of people who lost their discretionary medical cards in the recent controversial review have now had them returned.
It has told the Oireachtas Health Committee that around 10,000 people have received their cards back after the review.
Officials say the remaining 5,000 people affected will have their cards back by the end of next week.
White's comments come after the announcement last night that people over 70 will be given free GP cards as part of the agreement between the Taoiseach Enda Kenny and new Tánaiste Joan Burton.
Meanwhile, the minister responsible for primary care insists free GP care for under-6s will happen.
Alex White's comments come after the IMO said the government's plans for the scheme were 'falling apart'.
The Department of Health has not yet begun talks with doctors on the plans, while the government yesterday lost a vote in the Seanad connected with the issue.
But junior minister Alex White insists under-6s will soon get free access to a doctor:
White's comments come after the announcement last night that people over 70 will be given free GP cards as part of the agreement between the Taoiseach Enda Kenny and new Tánaiste Joan Burton.