Native Americans in national costumes, alongside demonstrators with banners reading "Save Bears Ears", "Protect Wild Utah" and "Hands off Utah", called for the monuments to be preserved.
Trump had asked Zinke to reassess the status of more than two dozen monuments established since 1996.
But the plan faces opposition from environmentalists and tribal leaders, who have decried it as illegal and an affront to Native Americans.
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It was reported that the plan would be announced by US President Donald Trump when he visits Utah next Monday, Xinhua news agency reported.
The two monuments were designated by former presidents Barrack Obama and Bill Clinton respectively.
Bears Ears presently a 1.3-million-acre monument in Utah's San Juan County, would be divided into the Indian Creek National Monument and the Shash Jha National monument. The plan would cut the overall size of Bears Ears from 1.35 million acres to 201,397 acres and Grand Staircase-Escalante from almost 1.9 million acres to 997,490 acres.
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The spokeswoman, Heather Swift, declined to offer any other details.
Attorney general for the Navajo Nation, Ethel Branch, said Trump should visit the monuments before making a decision on them.
Hatch said in a statement Thursday that 'details of the president's announcement are his and his alone to share, ' but added: 'I appreciate his willingness to listen to my advice and even more importantly, to give the people of Utah a voice in this process'.
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The President is expected to "shrink" the monuments in a Salt Lake City event on Monday. When inquired about the maps and advanced alterations a mouthpiece for the interior department that administers national monuments and public lands said that they are shoving imprecise information.