Last year, more than half a million people braved the so-called Darien Gap, where they faced perilous river crossings and violent criminal gangs that extort, kidnap and abuse them.
"We're going to close the Darien and we're going to repatriate all these people," Jose Raul Mulino told reporters during a visit to a working class suburb of the capital, without saying exactly how he would do it.
"I hope and trust that the United Nations (Refugee Agency) will help us," he added, pledging to respect migrants' human rights.
Along with other international groups and non-governmental organizations, the UN agency has personnel in the jungle helping migrants.
While most of those crossing the Darien are fleeing an economic crisis in Venezuela, migrants from Africa and Asia also enter the remote rainforest in a bid to reach the United States.
"The border of the United States, instead of being in Texas, moved to Panama," said Mulino, who served as security minister during Ricardo Martinelli's 2009-2014 presidency.
Mulino underscored the need for Panama to work with the United States and Colombia to tackle the problem.
With less than three weeks to go before the May 5 election, Mulino enjoys voter support of 34 percent, according to a survey by the Doxa firm published on Monday.
That puts him comfortably ahead of center-right lawyer Ricardo Lombana with 15 percent and former social democratic president Martin Torrijos with 13 percent.
Panama's electoral tribunal last month annulled the candidacy of Martinelli, a month after he lost his last bid to avoid prison and took asylum in the Nicaraguan embassy.
