In his address to the Maine Republican convention, wherein the party selected its delegates for the July national convention, Page alleged that foreign workers are being used in local restaurants.
LePage said workers from India are "hardest" and "the worst ones" to understand and one has to get an interpreter to talk to an Indian. However, he then quickly described Indians as "lovely" people.
LaPage's remarks came a day after Republican presidential frontrunner Donald Trump mocked Indian call centres but described India as a "great place".
Maine is a small northeastern state in the US.
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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.