The allegation against Sarkozy came from a former accountant to L"Oreal heiress Liliane Bettencourt that she gave 190,000 dollars in cash to Woerth, party treasurer, during the 2007 presidential campaign.
The alleged sum would greatly exceed legal limits for campaign donations.
Sarkozy had denied the claims, which have not been proven. French prosecutors have opened a preliminary investigation.
The allegation threatened the government"s credibility as it fights for unpopular cost-cutting reforms.
The President said Labour Minister Eric Woerth, who is at the heart of the scandal, would keep his job in the government.
But apparently bowing to public pressure, Sarkozy said he advised Woerth to resign from his contested second job, as the treasurer of their conservative UMP party.