Speaking in London later, Clinton promised the US would do everything it could to build on the "milestone" that the two countries had achieved by signing the protocols.
Armenia's foreign ministry said that the delay had been provoked by "unacceptable formulations" in a speech to be given by Turkey's top diplomat, but gave no details of what those formulations might be.
Clinton, who declared herself "very pleased" that the protocols had been signed, said that both countries had concerns that had delayed the signing ceremony.
The accord is the culmination of more than a year of Swiss-mediated talks.
Besides Clinton, Sergei Lavrov, the Russian foreign minister, and Bernard Kouchner, the French foreign minster, were among those present at the ceremony.
The protocols would still need ratification by their respective parliaments after being signed.
That endorsement will have to come as nationalists on both sides protest the accord, particularly an Armenian diaspora which is demanding that Turkey acknowledge the killings of 1.5 million Armenians during World War I as genocide.
Turkey has disputed the claims of genocide, with support from the US and UK, saying that the real death toll is lower.
Many Turks see the fighting as a civil war caused by the collapse of the Ottoman Empire during which an unverifiable number of Turks also died - although both sides agree that more Armenians than Turks were killed.
Both governments have majorities in parliament but are expected to hold back on immediately ratifying the protocols due to the opposition.
Speaking to Al Jazeera, Styopa Safaryan, an Armenian MP for the opposition Heritage Party, said: "At the very beginning, we welcomed this process, hoping that it will bring together Armenian and Turkish sides to provide an open and honest conversation on contemporary and historic issues.
"But after the disclosure of the signed protocols after August 31, we were surprised to see that non-directly, Turkish pre-conditions were on the table ... [Yet] there are no Armenian preconditions.
"That is why yesterday we had a huge demonstration in Armenia. People marched to the memorial of the Armenian genocide. People said no to protocol."
Al Jazeera's Anita McNaught, reporting from Karakoyunlu on Turkey's border with Armenia, said: "These protocols are powerful, but they have no legally enforceable status.
"They are reliant on the goodwill and moral authority of the parties who are the participants in it.
"What happens next is ratification ... they've got to sell this to their people and the politicians.
"If they push it though and they ratify it in parliament, we see two things: immediately, the establishment of diplomatic relations; then within two months the opening of borders."
For now, however, the question of reconciliation remains contentious at the very least.
As many as 10,000 people marched from Yerevan, the Armenian capital, to a hilltop memorial to World War I-era massacres on Friday to condemn the accords, some carrying placards reading "No Concessions to the Turks".
The move is expected to help Ankara in its bid to join the EU, while Armenia may benefit from closer ties to the West and greater economic openness with Turkey.
The issue of the disputed enclave of the Armenian-majority enclave of Nagorny-Karabakh also complicates the situation.
The enclave broke away from Azerbaijan after a war in the early 1990s, with Turkey closing its borders with Armenia in support of Azerbaijan in 1993.
"Constructive" talks were held between the Armenian and Azerbaijan presidents were held this week however, the former's office said on Friday.
Our correspondent said that Turkey and Armenia are looking towards future economic benefits of any accords, particularly the exploitation of oil and gas in the Caspian region.
"Turkey's ambition is to be the central collecting point for all the massively important pipelines that will start to draw increasingly - as the years roll on - the so-far untapped oil and gas reserves in the area," she said.
"It will completely change the game in this region and the fortunes of the various countries. But of course if Turkey didn't have a relationship with Armenia, it couldn't build pipelines through the area.
"The game plan, longer term, for both countries is, this should be one of their business options."
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