After reports on Wednesday in the left-wing Mediapart website, De Rugy was summoned to Prime Minister Edouard Philippe's office on Thursday.
The minister has been told to submit details of his expenditure to the parliamentary authorities and he has agreed to repay "every contested euro."
The website said de Rugy had hosted a dozen luxury dinners with little connection to his then position as Speaker of Parliament between 2017 and 2018 at the Speaker's official residence.
De Rugy did not deny hosting the dinners, but vigorously rejected the claim they had been purely social events not linked to his job at the National Assembly.
He slammed the articles as "misleading" and "tendentious".
Mediapart alleged that the events were essentially organised by his journalist wife Severine de Rugy for their circle and included luxuries such as champagne, vintage wines costing up to 500 euros a bottle, and giant lobsters.
The left-wing website published images of De Rugy posing at a candlelit table and his wife with a 500-euro, 2004 Mouton-Rothschild bottle of wine.
Prime Minister Edouard Philippe has also ordered an inspection of renovation work in de Rugy's official appartment after allegations in Mediapart of massive overspending on recent work.
The reports come as the centrist government of President Emmanuel Macron looks to recover from six months of anti-government protests sparked by economic inequality and claims that French leaders are out-of-touch with ordinary people.
De Rugy, who is from an aristocratic background, is a former environmental activist who joined Macron's party during his successful bid for the presidency in 2017.