Sen. Rand Paul warned President Trump Tuesday that running the government “by emergency” may only grow opposition against him as he threatens to raise tariffs on Mexican products in the coming week.

“Really tariffs [and] laws have to originate with Congress. You can’t just declare emergencies on spending, on tariffs,” the Kentucky Republican said on CNN’s “Right Now” show.

“I think what we may be finding is if we try to run government by emergency, is it may solidify opposition. Even people like myself who are largely supportive of President Trump, largely supportive of his initiatives. I can’t be for letting the president have all the power that the Constitution gave to Congress,” he said.

Mr. Paul said the Senate may be able to get enough votes to have a veto-proof majority and block the new tariffs, which could rise up to 25% in the coming months.

“I really do think that there may be enough numbers of people who think that we shouldn’t be allowing one person to make this decision, that we may have enough members to override a veto,” the senator said.

Mr. Trump said during a joint press conference with British Prime Minister Theresa May that he will not retreat from his threat to impose tariffs on Mexican products until Mexico does more to stem the flow of migrants puncturing the southern U.S. border.

He added it would be “foolish” for Republicans to pushback on the tariffs.

Mr. Paul has previously called tariffs “taxes that punish American consumers and producers” and said Mr. Trump is misusing the emergency declaration system.

“I can’t vote to give the president the power to spend money that hasn’t been appropriated by Congress,” he said earlier this year on Mr. Trump’s border wall declaration.

• Tom Howell Jr. contributed to this article.

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