Story highlights Carson traveled to the island territory to address a statehood advocacy group convention

Carson's views are similar to those of Republican rivals Jeb Bush and Marco Rubio

(CNN) Republican presidential candidate Ben Carson endorsed statehood for Puerto Rico at a Sunday campaign event on the island.

"In a Carson administration, I will leave no stone unturned in my efforts to secure this important step in Puerto Rico's history -- establishing Estado 51," said the retired neurosurgeon, highlighting the strategic benefits of the Caribbean island's location relative to the United States mainland.

Amid mounting scrutiny recently over his past, Carson traveled to the island territory to address a statehood advocacy group convention. The campaign estimated that 3,500 people were attended the New Progressive Party rally, at the Waldorf Astoria hotel.

"Mis hermanos Americanos, my campaign is built around the premise of 'We the People,' and through such lens, I view the statehood question in Puerto Rico as settled," Carson said, referring to a 2012 referendum in which a majority of island voters backed making Puerto Rico the 51st state.

Carson's statehood advocacy is generally inline with Republican presidential candidates from Florida, the state closest to Puerto Rico. Former Gov. Jeb Bush and Sen. Marco Rubio have said they would back Puerto Rico statehood if that's what island residents want.

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