Marx rejected Fiat Money

This can be clearly seen from Marx’s statement in Chapter 3 of volume 1 of Capital:

“The State puts in circulation bits of paper on which their various denominations, say £1, £5, &c, are printed. In so far as they actually take the place of gold to the same amount, their movement is subject to the laws that regulate the currency of money itself. A law peculiar to the circulation of paper money can spring up only from the proportion in which that paper money represents gold. Such a law exists; stated simply, it is as follows: the issue of paper money must not exceed in amount the gold (or silver as the case may be) which would actually circulate if not replaced by symbols. Now the quantity of gold which the circulation can absorb, constantly fluctuates about a given level. Still, the mass of the circulating medium in a given country never sinks below a certain minimum easily ascertained by actual experience. The fact that this minimum mass continually undergoes changes in its constituent parts, or that the pieces of gold of which it consists are being constantly replaced by fresh ones, causes of course no change either in its amount or in the continuity of its circulation. It can therefore be replaced by paper symbols. If, on the other hand, all the conduits of circulation were to-day filled with paper money to the full extent of their capacity for absorbing money, they might to-morrow be overflowing in consequence of a fluctuation in the circulation of commodities. There would no longer be any standard. If the paper money exceed its proper limit, which is the amount of gold coins of the like denomination that can actually be current, it would, apart from the danger of falling into general disrepute, represent only that quantity of gold, which, in accordance with the laws of the circulation of commodities, is required, and is alone capable of being represented by paper. If the quantity of paper money issued be double what it ought to be, then, as a matter of fact, £1 would be the money-name not of 1/4 of an ounce, but of 1/8 of an ounce of gold. The effect would be the same as if an alteration had taken place in the function of gold as a standard of prices. Those values that were previously expressed by the price of £1 would now be expressed by the price of £2.

Paper-money is a token representing gold or money. The relation between it and the values of commodities is this, that the latter are ideally expressed in the same quantities of gold that are symbolically represented by the paper. Only in so far as paper-money represents gold, which like all other commodities has value, is it a symbol of value.” (Marx 1906: 143–144).

So what Marx is saying here is as follows:

(1) paper money represents gold to the same amount as its face value;

(2) the paper money has to be backed by the same amount of gold, and if the state pumped out vast amounts of paper money in excess of the gold reserves, the standard of value would collapse (or as Marx says, “There would no longer be any standard”);

(3) paper money represents gold and it is clearly implied here that it needs to be officially convertible into gold at a fixed rate.

This rules out fiat money, and it is obvious that Marx was a metallist.

BIBLIOGRAPHY
Marx, Karl. 1906. Capital. A Critique of Political Economy (vol. 1; rev. trans. by Ernest Untermann from 4th German edn.). The Modern Library, New York.