Justice officials in Lima, the Peruvian capital, said a Peruvian court had begun extradition proceedings against the two Chilean officers, as the government launched an official inquiry.
The Chileans, identified as Daniel Marquez Torrealba and Victor Vergara Rojas, were allegedly working with an officer of the Peruvian air force, Victor Ariza Mendoza, whose detention was announced by officials on Thursday.
News reports said that Ariza, who worked in 2002 in Peru's embassy in Santiago, the Chilean capital, has been charged with "revealing state secrets, money laundering and espionage" on behalf of Chile since September 2005.
Prosecutors said Ariza, who reportedly confessed, would have earned $3,000 a month for his involvement in passing on information.
The authorities said they were also looking into the possible involvement of another Peruvian military officer in the case.
The row prompted Garcia on Saturday to cancel planned talks with Bachelet and quit a regional Pacific summit in Singapore a day early.
"I am returning 24 hours earlier than scheduled, so I can obtain complete and sufficient information (on the issue) and to be able to speak from Peru," Garcia said in Singapore at the Asia-Pacific Economic Co-operation (Apec) summit.
"We have to cancel [the meeting with Bachelet] because we are going back to Peru over this issue."
Speaking in Singapore on Friday, Jose Antonio Garcia Belaunde, Peru's foreign minister, decried an "offensive act" by Chile and called on Santiago to launch "an investigation into who in Chile gave the order" behind the alleged spying.
Garcia Belaunde said Peru's ambassador in Santiago would return home for consultations, but ruled out a break in bilateral relations.
The rift is the most serious in years between the two neighbours, which have had a long-running dispute over their maritime border in the Pacific Ocean.
Peru last year brought a claim before the International Court of Justice over territory lost to Chile in an 1879-1883 war.
Peru claims an area of about 100,000sq km in the Pacific Ocean that is currently under Chilean control.
For its part, Chile says the maritime border was settled by treaties in 1952 and 1954 - treaties that Lima argues were meant to regulate fishing, not demarcate the border.