It said world refined copper production was 2.07 million tonnes, compared with usage of 2.14Mt.
ICSG said preliminary data had indicated an apparent surplus.
"In the first four months of 2021, the world refined copper balance, based on Chinese apparent usage (excluding changes in unreported stocks), indicated a surplus of about 70,000t," it said.
It said preliminary data pointed to world copper mine production rising by 4% in the first four months.
Output from Chile, the world's leading copper producing country, was down 2% for the period but it was up 10% in Peru, the second biggest producer.
"However [Peru's] January-April 2021 production is still 17% below that of January-April 2019," it noted.
The group said Indonesian output had increased by about 80% mainly due to the continued ramp-up of underground production at the Grasberg mine.
ICSG said global demand remained below pre-pandemic levels in most countries.
World ex-China refined copper usage was estimated to have declined by about 9% in 2020, while Chinese apparent usage had increased by about 9%, it said.
ICSG said copper's average price this year was US$9,092.01/t, 47% above the 2020 annual average, thanks to the May record of $10,724.50/t.