BRUSSELS — European Union authorities on Tuesday proposed taking control of border and coastal security at entry points for migrants in countries like Greece and Italy, to get a grip on a crisis that has divided the bloc and fed the rise of populist political movements.

Officials at the European Commission, the executive arm of the European Union, said the centralized approach to border security would bolster confidence that the union can manage the migration crisis and would save one of its flagship policies — the Schengen rules that allow the free movement of citizens across most of Europe’s internal borders.

The proposal was expected to be discussed at a summit meeting of the national leaders of the European Union’s 28 member states in Brussels on Thursday.

Like the long effort to save the euro that began six years ago, the migration crisis is mainly focused on pushing one country, in this case Greece, to abide by European Union rules in exchange for greater support from other countries, namely Germany, that fear the repercussions of problems on the union’s periphery.