Non-OPEC compliance, however, has so far been modest, the minister told reporters outside parliament.
Under a deal signed last year, OPEC and non-OPEC countries agreed to reduce output by around 1.8 million barrels per day (bpd) as part of a concerted effort to curb a global oil glut.
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"Saudi Arabia reduced its production higher than its share," to boost confidence in OPEC's move, the Kuwaiti minister said.
He said that non-OPEC compliance was between 50 per cent and 60 per cent.
Independent oil producers agreed to cut their production by 558,000 bpd, of which Russia pledged to reduce 300,000 bpd.
Marzouk said the OPEC and non-OPEC Joint Ministerial Monitoring Committee will meet in Kuwait on March 26 to assess compliance.
Energy and oil ministers of Russia, Saudi Arabia, Venezuela, Oman and Algeria in addition to the OPEC secretary general are scheduled to attend.
Russia has said it will fully comply with the agreed cut by the end of April.
Oil prices are now up to 20 per cent higher than they were three months ago.
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