The treaty was signed by representatives of 66 countries on Monday - the first day that the treaty was open to signatures.
A joint statement was issued by the seven co-sponsors of the treaty - Argentina, Australia, Costa Rica, Finland, Japan, Kenya and the UK, saying they were "heartened" that so many countries had signed so early.
Signatory nations whose parliaments ratify the treaty would be required to examine the possibility that any deal risked breaching an international embargo, violating human rights laws, or allowing terrorists or criminals access to weapons.
German Foreign Minister Guido Westerwelle, who signed the treaty on Monday afternoon in New York, said the event "sends a strong signal to the international community" that there was widespread support for the treaty. However, he added that "more is needed."
The United States, which is the world's biggest arms and ammunition exporter, was not among the first signatories because of problems in agreement on a translation of the treaty into the UN's official languages.
"The United States welcomes the opening of the Arms Trade Treaty for signature, and we look forward to signing it as soon as the process of conforming the official translations is completed satisfactorily," said US Secretary of State John Kerry.
"The treaty is an important contribution to efforts to stem the illicit trade in conventional weapons, which fuels conflict, empowers violent extremists, and contributes to violations of human rights," Kerry said.
Abstentions - and opposition
The treaty was overwhelmingly approved by the UN General Assembly in April, although exporters Russia and China abstained and have not indicated that they will sign it. Neither have weapons importers Egypt and India. Iran, North Korea and Syria - which all face arms embargoes - were the only countries to cast no votes in the April ballot.
The treaty will only come into effect when 50 signatory countries have ratified it. Finnish Foreign Minister Erkki Tuomioja predicted this would happen "within slightly more than a year."
However, Tuomioja also said: "The real test is, of course, getting those who still have doubts or who have not made up their minds, to sign on and ratify."
The international arms market, which is currently under no international control, is estimated to be worth up to $85 billion (65 billion euros) per year.
rc/msh (AFP, AP, dpa)