MEXICO CITY—Influential Mexicans are pushing an aggressive and perhaps risky strategy to fight a likely increase in deportations of their undocumented compatriots in the U.S.: jam U.S. immigration courts in hopes of causing the already overburdened system to break down.

The proposal calls for ad campaigns advising migrants in the U.S. to take their cases to court and fight deportation if detained. “The backlog in the immigration system is tremendous,” said former Foreign Minister Jorge Castañeda. The idea is to double or triple the backlog, “until [U.S. President Donald] Trump desists in this stupid idea,” he added.

Mr. Castañeda is part of a group of Mexican officials, legislators, governors and public figures planning to meet with migrant groups Saturday in Phoenix to lay out plans to confront the Trump administration’s deportation policy.

Mexico’s government hasn’t endorsed the strategy or the group’s Phoenix mission. But it recently allocated some $50 million to assist undocumented migrants facing deportation, and President Enrique Peña Nieto has instructed the country’s 50 consulates in the U.S. to defend migrants.

Mexico’s Foreign Ministry said late Thursday it has intensified efforts to protect Mexican migrants, “foreseeing the hardening of measures by immigration authorities in the U.S., as well as possible constitutional violations during raids or in due process.”