The three main banks, the credit unions and An Post have now opened nearly 300,000 personal current accounts so far this year, according to Banking and Payments Federation Ireland.
The bulk of the new account openings are understood to have been with the three main banks: AIB, Bank of Ireland and Permanent TSB.
Close to 50,000 of the new account openings are in credit unions, the Irish League of Credit Unions said.
Approximately 500,000 current account holders need to find new providers for day-to-day banking with the imminent departure of KBC and Ulster Bank from this market.
Banking sources said the pace of bank account openings was catching up after a slow start earlier this year.
They pointed out that some people have yet to be notified by Ulster Bank or KBC that they have six months to close their account and open one with another provider.
An average of 11,000 new accounts per week are being opened in the three main banks, credit unions and An Post.
Two payments services organisations for credit unions and An Post are members of Banking and Payments Federation Ireland.
The banking group said the number of consumer current account openings continued to grow through June and into early July.
About 71,000 personal current accounts were opened in the four weeks ending July 8.
This is up from 56,000 in the previous four weeks. And it is more than double the total in the four weeks to April 15.
The banking federation said its members have now opened 297,000 personal current accounts this year, up to July 8.