As his impeachment trial was getting underway in the Senate, President Trump gave a hat tip Thursday to his evangelical base by updating the federal guidance on prayer in public schools — an action that came on National Religious Freedom Day.

The order is similar to a 2003 guidance on school prayer, but it establishes a state-mandated filing process for complaints against local schools and school districts.

States must then send the federal government a list each year of local schools and districts that have "a policy that prevents, or otherwise denies participation in, constitutionally protected prayer," in public schools. States are also required to report local schools that do not certify to the state that they don't have unconstitutional prayer policies.

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“You have things happening today that 10 or 15 years ago would have been unthinkable,” Trump said in response to a question about his views on the culture wars. “Taking the word God down, taking the word Christmas out. I think we’ve turned that one around very good. I think we’ve turned both of them around very good.”

The new Trump guidance also emphasizes that students may pray or read scriptures when they have free time during school. What is does not do is attempt to encourage schools themselves to sponsor prayer, acknowledging that teachers and administrators are generally barred from engaging in religious speech as part of their official duties or inviting religious speakers on behalf of the school.

"For example, teachers and other public school officials, acting in their official capacities, may not lead their classes in prayer, devotional readings from the Bible, or other religious activities," the guidance states. But, the order continues, "students and teachers do not 'shed their constitutional rights to freedom of speech or expression at the schoolhouse gate."

The guidance, citing Supreme Court precedent, makes clear students may pray alone or together during school, and that they may attempt to persuade their peers about religious topics just as they are allowed to with political topics.

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Before the school prayer event on Thursday, the Trump administration also proposed nine new rules that aim to ensure fair treatment of religious organizations by the federal government.

"The proposed rules would eliminate burdensome Obama-era requirements that unfairly imposed unique regulatory burdens only on religious organizations," a White House press release said.

Equal treatment of religious organizations has been a hot topic in recent months, especially with the Supreme Court set to hear arguments in a case next week about whether states may ban private religious schools from receiving public funds that are generally available to private, non-religious schools.

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These regulatory updates drew criticism from some groups that said the changes risked empowering discriminatory behavior in the name of religious freedom.

“These rules undermine the civil rights and religious freedom of millions of our most vulnerable Americans who rely on social services — with particularly dire consequences for LGBTQ people and religious minorities,” said Rachel Laser, president and CEO of Americans United for Separation of Church and State.

But Johnnie Moore, an evangelical adviser to the administration, lauded the moves as a fresh sign of Trump’s commitment to religious freedom.

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“The White House isn’t saying whether one should pray or to whom or what they should pray to,” Moore said. He added that “they are simply making it clear that in the United States students have First Amendment rights also, and our `separation of church and state’ wasn’t intended to suppress a vibrant religious life in America but to facilitate it.”

Fox News' Caleb Parke and The Associated Press contributed to this report.