Kuwait Oil Minister Essam al-Marzouk, who heads a joint ministerial committee tasked with overseeing compliance to the cuts, said conformity to the reductions could be improved.
"We need to see conformity across the board," to 100 percent, he told the opening session of the one-day meeting, which includes Russia, Venezuela, Oman, Algeria and Iraq.
The cuts aim to reduce world oil supplies and boost prices that had crashed since mid-2014.
Marzouk said that if OPEC and non-OPEC producers fully complied to the historical deal reached last year, "we may see a rebalance in the market in the third quarter of 2017."
Marzouk warned that crude oil stocks remained high and price volatility was on the rise.
The ministerial committee, of which non-OPEC Russia is co-chair, will also look into potentially recommending the output cuts deal be extended at a joint OPEC and non-OPEC meeting scheduled for May.
Bloomberg News reported that Venezuela, Oman and Iraq voiced support in Kuwait for a rollover of the cuts beyond June.
At the end of November, the Organisation of Petroleum Exporting Countries agreed to cut output by 1.2 million barrels per day (bpd) from January 1, initially for a period of six months.
Non-OPEC producers led by Russia agreed in December to cut their own output to 558,000 bpd.
Marzouk said earlier this month that OPEC compliance to the cuts had exceeded the 100 percent target but non-OPEC conformity remained moderate at between 50 percent to 60 percent.