"The agreement needs to be extended as we will not reach the desired inventory level by end of June", Saudi Arabia's Khalid Al-Falih said during the event with Russia's Alexander Novak.
The ministers will consult with other oil-producing countries with "the goal of reaching full consensus on the 9-month extension" they are seeking, the statement said.
WTI Crude is now trading up 3.03 percent at $49.29 per barrel, with Brent Crude up 2.93 percent at $52.33 (1126GMT).
Kuwait joined Saudi Arabia and Russian Federation in supporting an extension of oil-output cuts by OPEC and other global producers through the first quarter of 2018 to help trim global stockpiles.
"At this level, there isn't too big a correlation between oil and equities but since we've seen oil fall quite a bit in a month or so, today's rally in oil is helping the market grind higher", said Randy Frederick, vice president of trading and derivatives for Charles Schwab in Austin, Texas.
Saudi Arabia and Russian Federation have agreed to extend the Opec and non-Opec oil output reduction deal for another nine months until march 2018, reports said.
While traders and analysts doubt producers sticking to a prolonged cutback, the strong wording of the announcement had an impact on the market.
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The ministers agreed the deal should be extended through the first quarter of 2018 at the same volume of reductions, they said.
us production is now forecast to average about 9.31 million bpd this year - a level reached already, according to government figures. At the same time, the IEA continues to expect that world demand for oil in 2017 will grow by 1.3 mln barrels per day against the figure of 2016.
Following the Russia-Saudi statement, Kazakh Energy Minister Kanat Bozumbayev said "Kazakhstan should follow the trend", in comments reported by Russia's RIA Novosti agency.
This rise in the stock market for oil and other commodity products is expected to replace the shocking events that had occurred the other week which included the missile testing by North Korea and the cyber attack which damaged more than 2,00,000 computers in more than 150 countries.
But, this would depend on how much low-priced USA shale producers would raise production. "Get prepared for real sacrifices or we will have to say goodbye to the deal", he said.
"We believe that the market won't be able to balance by the year-end", he said. USA output has risen more than 10% since the middle of previous year, and data released on Friday by oil services firm Baker Hughes showed that the number of active rigs across the country rose for the 17th week in a row.