LIMA, Peru (Reuters) -- Former Peruvian President Alan Garcia has a strong early lead in Peru's presidential run-off race, with less than a month to go before election day, according to a survey released on Sunday.

In its first poll since run-off campaigning officially began this week, pollster Apoyo said Garcia had 57 percent support, while nationalist former army commander Ollanta Humala had 43 percent.

Peruvians will vote June 4 in the second round of the presidential race after no candidate won more than 50 percent in the first round in April.

Humala, who has worried international investors with pledges to rewrite tax contracts with foreign mining companies if elected, led the first round with 30.6 percent of the vote.

Center-left Garcia defeated conservative lawmaker Lourdes Flores in a tight race for second place after weeks of vote-counting.

"In Humala's case in the past week we have seen an apparent fall in support," Apoyo director Alfredo Torres said.

Another polling company, Datum, published a poll on Friday that showed Garcia with 56 percent support, compared with 44 percent for Humala, who is considered farther to the left.

Analysts say Garcia got a boost this week after Venezuelan President Hugo Chavez called Garcia "thief" and threatened to break ties with Peru if he won the presidency.

Humala was scheduled to meet on Monday with Bolivian President Evo Morales, a Chavez ally, near the border of the two countries.

Garcia's 1985-1990 rule ended in economic ruin marked by food shortages and 7,000 percent inflation, but his supporters say he has learned from his mistakes.

The methodology behind Apoyo's poll was not immediately available, but the pollster said the survey was taken at a national level and had a margin of error of 2.2 percent.