José Manuel Soria called a special news conference to announce that he had told Spanish prosecutors to get Panama to say whether he had "any stake, shares or even the least involvement with a company in this country".
He denied having any link with any Panamanian company, after online Spanish newspaper El Confidencial said that for two months in 1992 he was an administrator of a Bahamas-based offshore company named in the files leaked last week from law firm Mossack Fonseca.
Soria said the allegation was "false", the company was 100 percent British and his relationship with it was "commercial".
El Confidencial's claim prompted opposition Socialist party leader Pedro Sánchez to call for Soria's resignation.
The revelations in the Panama Papers, resulting from what the law firm blamed on a computer hack launched from abroad, revealed how the world's wealthy stashed assets in offshore companies.
Also on Monday, Spanish Justice Minister Rafael Catala said he did not consider Panama to be a tax haven.
"What it has is a different fiscal system, a different judicial culture," he told reporters.