TEL AVIV--De Beers Group said it would support stricter measures to keep conflict-tainted diamonds off the market, amid growing criticism of the global body tasked with stopping the trade in illicit stones.

Moves to more tightly monitor supply chains would be "fully" backed by De Beers, the world's biggest diamond producer and a key signatory of the Kimberly Process certification program, said Chief Executive Philippe Mellier.

"If there were more strict criteria we would be fully behind it because we want to protect the pipeline," said Mr. Mellier, who was referring to the global supply of rough, uncut diamonds rather than De Beers' own inventory.

De Beers, a unit of London-listed mining giant Anglo American PLC (AAL.LN), accounts for about 40% of the world's rough diamond output.

Along with rights groups and governments, De Beers was one of the architects of the Kimberley Process, a United Nations-backed program charged with stopping the trade in so-called blood diamonds.

However, some campaigners now say the body relies on self-regulation and defines conflict too narrowly, failing to take account of violence or human-rights violations by governments or groups supervising mining.

Global Witness, a non-governmental organization that helped establish the Kimberly Process, left the scheme in 2011, saying it is outdated because it doesn't address issues of human-rights violations by governments in diamond-producing countries.

Mr. Mellier pushed back against critics that argue the Kimberley Process no longer works, saying that it was an evolving system that had made a significant difference during the ten years of its existence, even if it could be improved.

"It's a huge success," said Mr. Mellier said. "For any process you always have people who say it could be tougher, better, and it could be better. But it's a huge achievement."

When the Kimberly Process was set up in 2003, about 15% of diamonds on the market were defined as conflict stones but that number has now fallen to around 1% of total world supply, said Mr. Mellier.

But despite early successes, a public rift has opened between some members of the Kimberly Process, which include representatives from the diamond business, governments from 80 countries, and non-government organizations.

The U.S. in May called for conflict diamonds to be more widely defined, saying that a less narrow designation could have allowed earlier intervention and saved lives in the Central African Republic, where rebels toppled the government in March. The poverty-stricken nation was eventually suspended from the Kimberley Process last month due to suspicions that the rebels, now in power, continued to be partly funded by the local diamond trade.

Other Kimberly Process participants have backed away from tighter controls.

Some African member countries have said stricter regulation could infringe on their sovereignty, while one of the original campaigners who helped establish the Kimberly Process argued that widening the definition of conflict minerals risks unwinding years of hard work.

"While the efforts of the NGOs and some governments are to be commended to redefine the definition of what are conflict diamonds in order to include diamonds that fund repressive regimes or are mined in areas where atrocities have been committed, it really does fall outside the purview of the Kimberley Process," said Alex Yearsley, director of consultancy firm Stanley Global Services.

"It is the responsibility of the diamond trade and importing governments to firstly not buy these diamonds but also not import them. Destroying the Kimberley Process in search of perfection is naive and they will regret it," said Mr. Yearsley.

--Francesca Freeman in London contributed to this report

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