Mr Gonzalez was responding to reporters' questions shortly before Spain's former Central Bank governor, Mariano Rubio, faced tough interrogation from the parliament's Economics Committee for alleged unethical and possibly illegal enrichment.
Despite detailed questioning, including an allegation that he bought shares in the big Banesto bank in 1987 knowing a takeover bid was likely and would probably boost their value, Mr Rubio evaded specific answers. 'I ordered my broker not to invest in banks. I don't know how that purchase could have happened,' he said.
At the press conference, the Prime Minister was asked: 'Are you really thinking of resigning. I don't think so but . . . ?' Mr Gonzalez interrupted with a smile: 'I think the same as you. I don't think I'm thinking of resigning.'
He added in a more serious tone: 'I can assure you we will get to the bottom of this (the Rubio case). Soon we will have all the data. Afterwards, it would be logical to see whether there are any political responsibilities, including, as you have indicated, my own. At the moment I'm not thinking about that.'
Mr Rubio, 62, headed the Central Bank for two successive terms between 1984 and 1992. He was appointed both times by Mr Gonzalez and was responsible to the then Finance and Economy Minister, Carlos Solchaga. Mr Solchaga's fate as leader of the Socialist Party's parliamentary group was likely to be dependent on the outcome of Mr Rubio's interrogation.
'He (Mr Rubio) is a public servant rigorous and honest with himself and with a great moral courage,' Mr Gonzalez said in 1992 after Mr Rubio completed his second term, amid allegations of unethical conduct linked with the failed bank Ibercorp.
The daily El Mundo recently published details of what it said was a secret account held on behalf of Mr Rubio during his term as governor and allegedly used to hide stock market gains. There was around 130m pesetas (pounds 600,000) in the account, according to the paper.
'Either this is a crass error or a pure trick,' Mr Rubio said.
Luisa Fernanda Rudi of the conservative Popular Party, said after Mr Rubio's responses: 'You have told us little or nothing new. Maybe you were just caught in the middle, innocent or guilty. We demand that Don Felipe Gonzalez take responsibility.'
Leaving little doubt that Mr Gonzalez's ruling Socialist Party was desperate to distance itself from Mr Rubio, the party's representative on the committee did not so much question as crucify the former Central Bank chief. The Socialist deputy, Juan Pablo Hernandez Molto, said: 'Your word has been put in serious doubt in this country. Mr Rubio, help yourself by helping us who are seeking justice.'
He accused Mr Rubio of 'creating lack of confidence in the entire financial system. This is your last chance. Take it, to save the little dignity you have left'.