In his address to the Maine Republican convention, wherein the party selected its delegates for the July national convention, LePage alleged that foreign workers are being used in local restaurants.
LePage, who is known for making controversial remarks, said it's hard to understand workers "from Bulgaria" workers from India are "the worst ones."
He also said that one has to get an interpreter to talk to an Indian. However, he then quickly described Indians as "lovely" people.
Meanwhile, both LePage and Trump suffered a setback at the Maine Convention, which elected 19 of the 23 delegates who are Cruz supporters.
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Maine is a small northeastern state in the US.
In his speech, LePage was highly critical of Cruz, accusing him of "stabbing us in the back".
"We reached a deal with Cruz's national campaign to put up a unity slate that would honour the wishes of the thousands of Mainers who voted at caucus. But Cruz's Northeast Political Director David Sawyer lied to us and broke the deal. Sawyer stabbed us in the back, reneged on the unity slate and betrayed the people of Maine," he said in a statement.
As of yesterday, Trump had 845 delegates against 559 of Cruz.
A candidate needs to have at least 1,237 delegates to earn the Republican presidential nomination.
Primaries are still to be held in 15 states, with the next round of primaries to be held in Maryland, Delaware, Philadelphia, Rhode Island and Connecticut on Tuesday.
Polls show that Trump is leading in all these states.