In the Communist Manifesto, Marx and Engels call for "Centralisation of credit in the hands of the state, by means of a national bank with State capital and an exclusive monopoly."

They were writing in an age where pretty much all European currencies were on some metallic standard, so they had a hard time imagining a true fiat currency. Marx also operated from a labor theory of value, which meant that he believed value could not be created purely by fiat.

However, Marx and Engels did call for the abolition of money ("abolition of buying and selling") in the Communist Manifesto. Lenin tried to do this directly during the Bolshevik Revolution by issuing a transitional fiat currency (sovznaks) whose value was "guaranteed by the full property of the state". (Just as today, a fiat currency's value is ultimately backed by the GDP of the country that issues it.) However, the wartime Soviet Union had very little property or economy to speak of, so the sovznak hyperinflated so quickly that a gold standard was reintroduced between 1922-1924. But the Soviet ruble was never really redeemable for gold by the general public, making it a fiat currency in all but name.