"Based on my judgement today, I think it is unlikely that we will need to continue" after June, Falih told reporters at an energy forum in Abu Dhabi.
"Demand will pick up in the summer and we want to make sure that the markets continue to be supplied well and we don't want to create a shortage or a squeeze," he added.
OPEC and non-OPEC oil producing countries agreed to cap production from January 1 to end a global glut that has hammered prices, but doubts remain about implementation before data is released at the end of the month.
"Of course, there are many variables that could come into play between now and June. At that time, we'll be able to assess," he said.
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Falih said all concerned producers have expressed "their willingness to extend if necessary".
"The extension will only happen if there is a need, and if there is a need we will do it," he added.
The United Arab Emirates' Energy Minister Suhail al-Mazrouei said Wednesday it was too early to consider extending the deal.