It's a story I've heard myself often. It's something of an exaggeration, it turns out.
The person reputed to have made the offer was Kyriakos Pittakis, who after Greek Independence became the first Greek General Superintendent of Antiquities. (He was not a good archaeologist by modern standards; but few archaeologists in 1832 were.) In 1821, he was 23, and part of the troops besieging the Acropolis (he was not involved in the second siege of the Acropolis in 1826: he had already left to study in Corfu.) The English Wikipedia article repeats the claim that:
He fought in the Greek War of Independence against the Ottoman Empire, besieging the Ottoman troops in the Acropolis; desperate for ammunition, the Ottomans began to dismantle sections of the Acropolis in order to recover the lead clamps which they intended to use for bullets. When Pittakis and his cohorts learned of this, they sent bullets to the opposing army, in hopes that the Acropolis would be spared such destruction.
The offer is proverbially set down in Greek as Να τα βόλια, μην αγγίξετε τις κολώνες, "Here's the bullets, don't touch the columns."
The Greek Wikipedia article, oddly enough, doesn't mention the episode at all, but Metapedia, a Greek Wikipedia competitor, says the claim was made by Alexandros Rizos Rangavis when he was delivering Pittakis' funeral oration in 1863.
This article refers to this as a "pious and probably unfulfilled hope" expressed by the young fighter. And this article rejects the notion that Pittakis' desire was more generally held by his fellow combatants, to the poin t of offering ammunition:
It appears to be true that Pittakis expressed the pious wish that he might be able to offer the Turks bullets so they would not destroy the monument. But the offer to the besieged Turks of 4000 okas [5 tonnes] of lead, so they would not destroy and crush the columns, is a grotesque falsification, often mentioned in national celebrations and school textbooks. After all during the next siege in 1826, the besieged, who this time were Greek, sought the same methods for finding ammunition as the formerly besieged Turks: they used the marble stones as bombs. [...]
The revolutionary government sent to Athens (March 1822) a team of foreign volunteers led by the French artillery colonel Olivier Voutier to coordinate the bombing. War minister Ioannis Kolettis, in a letter to the mission lead, asked him hypocritically, frivolously and impudently to take care that the cannonballs did not damage the monuments "and especially the Parthenon." And he adds: "we commend the masterpieces of our ancestors to your love of beauty." As if the hail of bombs falling on such a small area full of antiquities could target exclusively and precisely Turkish heads.
And the result was that Voutier's bombardment destroyed the monuments without damaging the Turks. Their losses during the siege were one old African slave. Who cared about the Parthenon during a war to the finish? The Athenians seeing the damage to the antiquities from Greek canons told the French officer: "We will sacrifice the monuments of our ancestors to achieve that freedom which will resurrect our Callicrateses."
The tone is tendentious, and Kolettis may have been just as naive as Pittakis, instead of hypocritical. Voutier's report, on the other hand, is authentic: he wrote about the incident in 1823, and reports that the Athenians themselves talked him out of any misgivings he had about the bombardment, and the harm both to Turkish civilians and to the antiquities, with those words. (And in the very next paragraph, he reports observing the Turks extracting lead from the columns of the Parthenon.)
Pittakis' wish is reported second hand in a eulogy, but does not seem to be disputed. The actual offer of lead by the besiegers, in light of Voutier's contemporary report, is implausible.
(Voutier is better known to history for discovering the Venus de Milo.)
