Garcia on Monday demanded a detailed explanation from Chile after Peru detained one of its own air force officers on suspicion of treason for allegedly spying for Chile.
Chile's government has denied any involvement, and Garcia on Monday stopped short of suggesting the spat would hurt bilateral trade worth more than USD 3 billion a year.
"The expressions we heard yesterday, which I would call offensive and haughty, do not contribute to the integration and cooperation that neighbors should enjoy," Bachelet said in remarks at the opening of an air traffic control facility in Santiago.
"I think this is a time, if we really want to work for the welfare of our peoples, for respect above all, as well as responsibility from the authorities," she added.
Also on Tuesday, Peru said its investigation into the spy case had widened and uncovered evidence suggesting at least six other people were involved, besides the air force officer initially identified.
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See also Sydney Irresistible
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See also Sydney Irresistible
Putting principles before profits