BROWNSVILLE, Tex. — President Biden and former president Donald Trump visited separate Texas border towns Thursday, blaming each other for a surge in illegal immigration and seeking to take the offensive on an issue that is shaping up to be a critical and volatile factor in this year’s presidential contest.

Biden used his visit in Brownsville, a Democratic stronghold, to blame Trump, the leading Republican presidential candidate, for killing a bipartisan border bill that would have provided $20 billion to hire thousands of new Border Patrol agents and asylum officers and increase detention capacity. The measure also would have included a trigger mechanism to effectively shut down the border, which Biden said he would have been willing to invoke.

Biden said the bill was on its way to passage until Trump “came along and said, ‘Don’t do that, it will benefit the incumbent.’ ” Biden said sarcastically, “It’s a hell of a way to do business in the United States of America.”

Addressing Republican members of Congress, Biden urged them to “show a little spine” and demonstrate independence from Trump. “Let’s remember who we work for, for God’s sake,” the president said.

About 300 miles away in Eagle Pass, Trump seized on an issue that was central to his rise in 2016 and that he has made a centerpiece of his third presidential campaign. “This is a Joe Biden invasion, this is a Biden invasion,” the former president said.

“The United States is being overrun by the Biden migrant crime,” Trump added. “It’s a new form of vicious violation to our country.” Experts say most of the evidence suggests that undocumented immigrants do not cause more crime.

The remarkable split-screen — the two presidential contenders each delivered their speeches at about the same time — provided a preview of what could be a long and vicious general election campaign.

Biden, who polls show faces widespread disapproval of his handling of immigration, has in recent weeks tried to take control of the issue by reminding voters that he embraced the bipartisan border measure. Republican lawmakers had demanded border security measures as part of a $100 billion-plus aid bill for Ukraine and Israel, but they refused to back the package after Trump said on Truth Social that passing it would be “another Gift to the Radical Left Democrats.”

Trump has long made immigration the focus of his “America First” agenda. He campaigned in 2016 on building a U.S.-Mexico border wall and has vowed to enact “the largest domestic deportation operation in American history” in a second term. He has repeatedly blamed Biden for a record number of apprehensions since 2021.

Trump has also used dehumanizing language to describe undocumented immigrants, suggesting that they are waging an “invasion” of the United States and accusing them of “poisoning the blood of our country,” drawing comparisons to Nazi rhetoric from civil rights experts and historians.

The two men chose border cities that reflect their dueling approaches to immigration. Brownsville is in sync with Democrats’ traditional approach of balancing border security with humanitarian considerations. Eagle Pass, by contrast, has become a symbol of Republican defiance against Biden’s handling of immigration. Texas Gov. Greg Abbott (R) seized a park in the city earlier this year, shutting out U.S. Border Patrol agents who had long used it as a staging point.

Illegal border crossings soared in the months after Biden took office, signaling a more relaxed policy and immediately rolling back many Trump-era restrictions. As immigration surged, Biden warned that he would still enforce immigration laws, and he temporarily kept in place a Trump pandemic policy known as Title 42 that allowed authorities to quickly expel border crossers.

Even so, the number of people taken into custody by the U.S. Border Patrol has reached the highest levels in the agency’s 100-year history under Biden, averaging 2 million per year.

A February Gallup survey found that voters ranked immigration as the single most important problem facing the country, followed by the government, the economy and inflation. A Marquette Law School national poll this month found 53 percent of registered voters saying Trump would do a better job handling the issue, while 25 percent said Biden would.

Frustrated by Congress’s inaction, Biden has been considering executive actions that could limit unauthorized migration and restrict the asylum process, according to administration officials who spoke on the condition of anonymity to discuss internal deliberations. But he did not announce any new actions Thursday.

It is not clear whether Biden’s border visit — along with his potential executive actions and newly fiery rhetoric — can change the political dynamic on immigration. But the White House hopes a tougher stance can at a minimum blunt Republicans’ advantage on the issue.

Trump’s immigration platform includes reinstating a travel ban that restricted people from several Muslim-majority countries from entering the United States. The Trump campaign has also said he would sign an executive order that would withhold passports, Social Security numbers and other government benefits from the children of undocumented immigrants, who are U.S. citizens.

As president, Trump signed executive orders to enact his travel ban, but it faced numerous court challenges and was significantly reduced in scope. The Trump administration also drew a backlash for a policy of separating migrant families.

Trump made building a border wall a central promise of his 2016 campaign, and his administration built more than 450 miles of new border fencing at a cost of $11 billion. Despite that construction, illegal border crossings surged from 500,000 per year in 2020 to more than 2 million per year.

Scott Clement, Nick Miroff, Maria Sacchetti and Arelis R. Hernández contributed to this report.