Peruvian Prime Minister Alberto Otárola said Saturday that the dialogue with governments of other countries has "advanced" in discussing what he calls a "migration crisis".
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Hundreds of people remain stranded, unable to cross into Peru in an effort to return to their home country of Venezuela.
The tension between migrants and Peruvian citizens seeking to cross to the Chilean side caused clashes with stones earlier Saturday.
One person has been injured.
Venezuelan consular authorities appeared in the area in an effort to help their compatriots.
The migrants have been facing the inhospitable climate of the Atacama desert, one of the most arid on the planet, with heat during the day and intense cold at night.
Most of them are not equipped for such adverse conditions.
Among the hundreds of migrants stranded, there are families with children and people in a highly vulnerable situation, according to international organizations, including the UN.
Chile said Friday it would start registering all the undocumented migrants who want to leave the country, and Peru started letting some of them through to its border offices.