The miners were working illegally at a project, which has had on average 2,000 illegal incursions onto its jurisdiction per day, the company said adding that further casualties were a possibility.
"The incident has no impact on production," Glencore said in a statement.
Glencore owns a 75% stake in the Kamoto Copper Company through its subsidiary Katanga Mining.
Kamoto produced 57,175 tonnes of copper cathode in the first quarter of this year, according to a statement on the Katanga Mining website.
Richard Muyej, the governor of Lualaba province, Democratic Republic of Congo, told Reuters earlier on today that 36 people had been killed.
The deaths come at a time of increasing scrutiny over the fractious relationships between major mining companies, such as Glencore, and their activities in many areas of central Africa, where often illegal artisinal mining is common.
Copper futures on the London Metal Exchange remained unchanged at $5,980 per tonne in the afternoon on June 27 following the news.
Glencore partially resumed sales and exports of the cobalt hydroxide produced at Kamoto in April this year, after high uranium levels forced a suspension from November 2018.
Glencore expects to produce about 26,000 tonnes of cobalt at Katanga in 2019. The majority of material is still being stockpiled, pending the implementation of an ion exchange to treat the high-uranium material on a long-term basis.
Artisanal cobalt production is believed to have dwindled significantly this year, however, due to falling prices.
Fastmarkets’ price assessment for standard-grade cobalt stands at $13.75-15.35 per lb, in-warehouse as of June 27, down from highs of $43.70-44.45 per lb in April last year.
Cobalt hydroxide payables – the percentage of the standard-grade low paid to procure hydroxide - is at 62-63%, compared with 67-69% at the beginning of May
Additional reporting by Hassan Butt in London