Twenty-four oil producing countries, including Saudi Arabia, other members of the Organization of Petroleum Exporting Countries and Russia, agreed in late 2016 to reduce output by around 1.8 million barrels per day (bpd).
The deal, since extended to March 31, 2018, was aimed at reducing a global oil glut that had seen crude prices plummet from over USD 100 a barrel in 2014 to a 13-year low of under USD 30 last year.
"We will look at the situation in late March. I think this is possible," he said.
If OPEC member countries agree on a further extension of the deal, it would be "at least until the end of 2018," Putin said.
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The Russian president spoke ahead of meetings with the leaders of key OPEC members, Saudi Arabia and Venezuela.
King Salman of Saudi Arabia will arrive in Russia later today for the first official visit to the country by a Saudi king.
The visits come a month before members of the OPEC oil cartel, of which Saudi Arabia is the biggest producer, are due to meet with the non-OPEC countries that have joined them in cutting crude output.