Protestors tried to storm the parliament in Taipei on Friday ahead of the Ma-Xi meeting, and the opposition leader, Tsai Ing-wen, has said the Singapore summit threatens Taiwan's democracy.
She leads the Democratic People's Party (DPP), which has a large pro-independence base of supporters, and is more sceptical of growing ties with the mainland.
Her likely election in January has been the impetus for the meeting, as many analysts believe such an exchange would not be possible if the DPP were in power.
Police prevent pro-Taiwan independence activists from burning portraits of the leaders.