"It is clear today based on the current level of production that we are approaching a very stable stage ... whether for the consumers or the producers," Bakhit al-Rashidi told reporters.
Kuwait has raised its oil output under June's agreement among the Organization of the Petroleum Exporting Countries and is pumping 2.8 million barrels per day, Rashidi said, adding that the country's production capacity is 3.1 million bpd.
An upcoming joint OPEC and non-OPEC committee meeting in Algeria, set for Sept. 22-23, will review producers' oil supply levels after OPEC and others led by Russia agreed in June to raise output to cool the market, the minister said.
OPEC and non-OPEC said they would raise supply by returning to 100 percent compliance with previously agreed output cuts, after months of underproduction. That would mean a roughly 1 million bpd increase in output.
Last month, Brent crude prices fell more than 6 percent and US crude slumped about 7 percent, the biggest monthly declines for both benchmarks since July 2016.
Rashidi said he hoped oil production from the Neutral Zone, which Kuwait shares with Saudi Arabia, would resume "very soon".
The Neutral Zone is the only place in Saudi Arabia and Kuwait where foreign oil firms have equity in oilfields, which are otherwise owned and operated by state oil companies. Crude output in the zone is divided equally between the two countries.
The joint Khafji oilfield was shut in October 2014 for environmental reasons, while the Wafra oilfield has been shut since May 2015 due to operating difficulties.