Mexican officials say labor provisions of the United States-Mexico-Canada Agreement (USMCA) include health protections for migrants regardless of immigration status.
The new restrictions are set to take effect in January.
The storm has left scores of people dead and over 100 others missing in Mexico and Central America after it made landfall as a category 4 hurricane.
The protesters threw molotov cocktails at officers in Mexico City on Monday during a demonstration marking International Safe Abortion Day.
In a 5-4 vote, the court rejected the request made by an environmental group and a border community group.
The proposal, which still needs further approval, will impose prison time on those who force others to undergo the medically denounced practice.
Some people have sought deportation due to fear of contracting COVID-19 inside detention facilities.
The Trump administration has taken multiple steps to speed up deportations and restrict access to asylum.
The president is receiving treatment and will work remotely and through his aides.
The virus poses an additional risk for rescuers and evacuees and will make it harder to persuade people to leave their homes, experts say.