The 192-nation body adopted a resolution warning that "trade in conflict diamonds continues to be a matter of serious international concern" and increased vigilance was vital.
The assembly was responding to a report on conflict stones by Namibia, which chairs the diamond industry’s Kimberley Process, a certification scheme set up in 2003 in the wake of devastating civil wars in Angola, Sierra Leone and Liberia.
Those wars were largely financed by the diamond trade.
Although the resolution was adopted, a number of Western delegations criticized the assembly for failing to mention concerns about Zimbabwe, which is suspected of not complying with Kimberley Process safeguards.
Namibia’s report to Secretary-General Ban Ki-moon said there were "credible indications of significant non-compliance with the minimum requirements of the (Kimberley Process) by Zimbabwe."
U.S. delegate Laura Ross said: "We regret that language reflecting this concern has not been included in the text of this resolution."
Speaking on behalf of the European Union, Sweden’s U.N. Ambassador Anders Liden voiced similar views, as did delegates from Japan, Australia and Canada.
Zimbabwe’s U.N. Ambassador Boniface Chidyausiku rejected the suggestion that Harare was not complying with the rules.
"We are committed to the Kimberley Process," he told the assembly, adding that the United States and others were trying to politicize the issue by attacking his country.
Zimbabwe was one of the resolution’s co-sponsors.
Before the implementation of the Kimberley Process, conflict stones made up about 15 percent of the world market. They are believed to account for less than 1 percent of stones traded today, although many diamonds remain untraceable.
The Namibian report warned that blood diamonds could be making a comeback. It said Internet sales and postal shipments "have become issues of concern, as it has proved difficult to track and reconcile rough diamond shipments."
In January, Israel replaces Namibia as the chair of the Kimberley Process. The United States, European Union and other Western delegations complained that the assembly resolution failed to welcome Israel’s 2010 chairmanship.
The adopted resolution simply "takes note" that Israel will chair the Kimberley Process. Bashar Ja’afari, the ambassador of Israel’s enemy Syria, proposed removing any mention of the Jewish state from the resolution, but his motion was defeated.
A United Nations panel of experts said in October that Israel, whose diamond trade is worth more than $10 billion, may be involved in the illegal export and sale of blood diamonds from Ivory Coast. Israeli officials rejected the accusation.