Mexico and Ecuador have brought complaints against each other at the international court, escalating a diplomatic feud.
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Mexico had earlier appealed to the UN court to sanction Ecuador for storming its embassy in Quito.
Mexico has a tradition of granting asylum, but experts see political motive behind offers made under Lopez Obrador.
Killing of Noe Ramos Ferretiz and Alberto Garcia bring to 17 the number of slain candidates ahead of June 2 polls.