Mexico promised Friday to step up its own border enforcement and to allow the return of some Central Americans who crossed its territory en route to the U.S., striking a deal to head off crippling economic tariffs President Trump had vowed to impose next week.

Both sides also promised to reevaluate the deal over the coming months and announce new steps in 90 days, if it turns out Mexico’s concessions this week aren’t enough to stem the flow.

Mr. Trump announced the deal on Twitter, saying he was satisfied enough to cancel the 5% tariff he was poised to impose.

“I am pleased to inform you that The United States of America has reached a signed agreement with Mexico. The Tariffs scheduled to be implemented by the U.S. on Monday, against Mexico, are hereby indefinitely suspended,” the president said.

Mexican officials confirmed the deal and joined the U.S. in a joint declaration laying out its terms.

Mexico promised to deploy its national guard throughout its territory, though with a special focus on its southern border. Mexico also promised to do more to dismantle the smuggling cartels and networks that bus, drive or shepherd by foot thousands of migrants a day from Central American to the U.S. border.

The biggest concession from Mexico is a promise to expand its cooperation with the Trump administration’s Migration Protection Protocols, a name the U.S. gave to its plan to make many Central American asylum-seekers who crossed Mexico return to that country and wait while their cases are being heard in U.S. immigration courts.

The goal is to change the incentive structure. The Central Americans generally want to reach the U.S. and make asylum claims as a way of gaining a foothold. Few will actually qualify, but once on U.S. soil they can disappear into the shadows.

If they are made to wait in Mexico, U.S. officials hope they lose the incentive to try the journey in the first place.

A smaller version of the MPP has been in effect for months, but under the new deal Mexico agreed to expand its cooperation border-wide. It will offer work permits, health care and humanitarian assistance to the migrants who get returned to its territory to wait.

The U.S. agreed to speed up its asylum cases as quickly as possible.

And both sides said they’ll continue to work to improve conditions in Central America, hoping to curtail the incentives pushing people to leave their countries.

The agreement does not, however, include Mexico signing a safe third country agreement. Under that deal, Mexico would have agreed to take back all asylum-seekers that traverse its territory en route to the U.S.

America has such an agreement with Canada, but Mexico, despite touting its human rights record, has balked at that step.

The question for Mr. Trump now will be whether the deal, whatever it is, can actually change the dynamics on the border.

American officials say some 5,000 migrants enter Mexico a day, but Mexico is blocking perhaps just one in five of them. That leaves some 4,000 a day to reach to U.S.

Even if the flow drops as the weather turns hotter — a usual, though not universal, phenomenon at the border — Homeland Security officials said this week they expect the numbers to remain above 100,000 a month.

That sets a baseline Mr. Trump must try to beat for him to claim success.

Republicans on Capitol Hill breathed a sigh of relief after the deal was announced. They’d been faced with the possibility of having to vote to block the president’s tariffs — a vote that might have succeeded.

Mr. Trump’s use of tariffs has left Republicans and many in the president’s activist political base weary.

The tariff threat had also threatened to derail any chance of passing the U.S.-Mexico-Canada free trade agreement Mr. Trump is seeking.

With a deal in hand, Republicans cheered their party leader.

“Once again, President Trump has proven those who doubted him wrong by getting Mexico to step up their efforts to help us secure our southern border,” said Rep. Steve Scalise, the No. 2 Republican in the House.

Sen. Thom Tillis, North Carolina Republican, said Mr. Trump “proved he wasn’t bluffing,” and praised his “bold leadership” for winning the concessions.

Democrats were slower to react Friday night.

Earlier in the week they had mocked Mr. Trump, predicting he would cave before his Monday deadline.

Yet Mexico took the president seriously, deploying its foreign minister for talks this week.

Those talks led to Friday’s deal.

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