De la Torre, whose team failed to defend the CONCACAF Gold Cup in the United States, would have his position reviewed again after the qualifiers, Justino Compean, president of the Mexican Football Federation, told a news conference.
Mexico had won the last two Gold Cup tournaments but were upset twice by Panama in their opening group match and in their semi-final last week.
"We don't justify the situation but there is still support for the present (coaching) administration," Compean said.
"There were voices who didn't agree ... I still believe (De la Torre's staff) is the best we have to take us to Brazil 2014.
"I asked (the board) for trust in the administration headed by Chepo (De la Torre), who has to recognise his mistakes."
Mexico also had a disappointing Confederations Cup in Brazil in June and have suffered from a chronic shortage of goals.
Expected to reach Brazil with ease, they are struggling in third place in the six-nation final qualifying group with eight points, scoring only three goals in their one win and five draws.
They meet fourth-placed Honduras in Mexico City on September 6 with a warm-up scheduled for August 14 against Ivory Coast.
The teams finishing in the top three places in the group will automatically qualify for the finals. The fourth goes into a playoff against Oceania winners New Zealand.
(Reporting by Carlos Calvo; Writing by Rex Gowar in London; Editing by Peter Rutherford)
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