The move follows several waves of anti-Muslim violence that have coincided with a groundswell of Buddhist nationalism.
While the proposals from Thein Sein, in a letter seen by AFP, are vaguely worded, they appear to call for some kind of restrictions on inter-faith marriages.
The proposals include a law "to give protection and rights for ethnic Buddhists when marrying with other religions", as well as a ban on polygamy and legislation to "balance the increasing population".
Thein Sein, who has won international plaudits for his political reforms, submitted the proposals to lawmakers after receiving a petition led by Buddhist clerics last year.
A radical monk called Wirathu has campaigned for a law to force non-Buddhist men wishing to marry a Buddhist woman to convert and gain permission to wed from her parents, or risk 10 years in jail.
"We have tried continually to have a national protection bill. Now it has started to come true with the president's message. We are so glad," Wirathu.
Opposition leader Aung San Suu Kyi has previously slammed his proposals as "a violation of women's rights and human rights".
Myanmar has already faced criticism from rights groups over a controversial "two-child policy" in parts of the western state of Rakhine.
Minority Rohingya Muslims in Rakhine face a slew of restrictions that have led the United Nations to consider them as one of the world's most persecuted people.
Two waves of deadly communal violence between Buddhists and Muslims in Rakhine in 2012 left more than 200 people dead and around 140,000 displaced, mainly Rohingya.
Sectarian bloodshed - mostly targeting Muslims - has since spread to other parts of the country and laid bare deep divides that were largely suppressed under decades of military rule, which ended in 2011.
Sources: ABC News/AFP