The new page prompts visitors to take action with Patagonia as they "stand alongside over 350 businesses, conservation groups and Native American tribes that have come together on this issue to protect public lands". The court cases are likely to drag on for years. The move comes a week after tribal leaders decried Trump's use of the name of a historical Native American figure as a slur.
Another lawsuit from three groups including the Society of Vertebrate Paleontology makes similar claims.
Navajo Nation Attorney General Ethel Branch says only Congress has the ability to downsize a monument.
Speaking in Salt Lake City Monday, Trumps said the move reverses "federal overreach" and will return control of land to local authorities and citizens.
Patagonia President and CEO Rose Marcario said the outdoor-apparel company will join an expected court fight against the monument reduction, which she described as the "largest elimination of protected land in American history".
Outside Trump's announcement Monday, roughly 3,000 protesters lined up near the State Capitol. A smaller group gathered in support, including some who said they favor potential drilling or mining there that could create jobs.
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In a statement Monday, NARF said: "President Trump's action to revoke and replace the Bears Ears National Monument is not only an attack on the five sovereign nations with deep ties to the Bears Ears region, it is a complete violation of the separation of powers enshrined in our Constitution".
Bears Ears, created almost a year ago, will be reduced to 201,876 acres (315 square miles).
The monument designated by President Bill Clinton in 1996 was almost 3,000 square miles (7,770 square kilometers). In April he ordered Zinke to identify which of 27 monuments designated by past presidents should be rescinded or resized.
Democrats and environmentalists accuse Trump and Zinke of engaging in a secretive process aimed at helping industry groups that have donated to Republican political campaigns. He was accompanied on Air Force One by Utah Senators Mike Lee and Orrin Hatch, who is contemplating whether to run for re-election next year when he'll turn 84. Hatch and other state Republican leaders pushed Trump to launch the review, saying the monuments designated by the former Democratic presidents locked up too much federal land. "They're wrong. The families and communities of Utah know and love this land the best, and you know the best how to take care of your land". He said the decision would "give back your voice". The lawsuit argues that Trump exceeded his authority by overturning congressional legislation that added land to the monument after Clinton's initial declaration.
Interior Department spokeswoman Heather Swift said Wednesday that Patagonia's claims are inaccurate because Zinke never took any private planes paid for by special interests.
The reasoning behind the move is to designate as protected "the smallest area compatible with the protection of the objects of scientific or historic interest", and the proclamation also opens the newly public lands to "disposition under all laws relating to mineral and geothermal leasing; and location, entry, and patent under the mining laws".
The administration is also considering shrinking national monuments in states like Nevada and Oregon.
Zinke also has recommended allowing logging at a newly designated monument in ME and urges more grazing, hunting and fishing at two sites in New Mexico.