Authorities in the strife-torn western state of Rakhine said last month that they had reaffirmed the longstanding rule -- which was first introduced during the junta era -- in two townships.
"The central government did not announce that policy. We will look into it," presidential spokesman Ye Htut told AFP.
"The population in that area is much higher than in other regions so there are some social and economic problems within each family."
The UN has called for an end to the ban, which it said was discriminatory and an infringement on human rights.
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Opposition leader Aung San Suu Kyi, who has been accused by activists of failing to speak up for the marginalised Rohingya minority group, last month criticised the policy as counter to human rights.
But highlighting the pressure she faces from within her movement, eight NLD offices in Rakhine have written to the party headquarters expressing support for the two-child policy, citing national security.
Myanmar views its population of roughly 800,000 Rohingya as illegal Bangladeshi immigrants. They are considered by the UN to be one of the world's most persecuted minorities.