President Joe Biden and Donald Trump have made competing visits to the US border in Texas, each seeking to stress they can tackle illegal immigration.
The issue is one of the most polarising in US politics, and will be central to this year's presidential election.
November's contest looks likely to be another showdown between the two men.
Mr Biden accused his Republican rival - who spoke of the "very dangerous" situation at the border - of hindering his efforts to crackdown on crossings.
Republicans in the House of Representatives have blocked bipartisan border reforms, in what Democrats say is an effort masterminded by Mr Trump to deny them a win before the election.
In Texas, Mr Trump said he would "take care" of the issue of illegal immigration if he was re-elected. He has previously promised mass deportations if he wins power again.
The issue is an intense focus because more than 6.3 million migrants have been detained crossing into the US illegally during Mr Biden's tenure - a higher number than under previous presidencies.
However, experts say the reasons for the spike are complex - with some factors pre-dating his government and sitting outside American control.
Why do so many migrants want to cross from Mexico to the US?
In his speech, Mr Trump said "thousands" of migrants from the Middle East and Africa were illegally crossing from Mexico. In fact, the majority of those caught doing so are from Latin America.
He also attacked what he has recently termed "Biden migrant crime", although there is no national data giving evidence of migrant-driven crime waves in US cities.
Supporters and protesters alike assembled during Mr Trump's visit to Eagle Pass, a Democrat-run town where Republicans are making political headway by attacking Mr Biden's running of the border.
Enriqueta Diaz, 81, told the BBC she backed Mr Trump's proposals to further militarise the border. "You have to follow the law," she said, pointing out that her own mother, a Mexican, had gone through a citizenship process herself.
Mr Trump met the state governor, Republican Greg Abbott, who has battled the federal government by trying to use powers of his own to halt illegal crossings - as well as bussing migrants to northern cities.
Meanwhile, Mr Biden - who quipped that he did not realise his "good friend" Mr Trump was due to visit Texas on the same day - headed to meet border officials in Brownsville.
Speaking after Mr Trump, he stressed the urgency of action and need for more resources to police the border. The bipartisan border reform bill had been "derailed by rank partisan politics", he said.
He launched a direct appeal to his rival to "join me" on the issue.
The president travelled to Texas with Homeland Secretary Alejandro Mayorkas, who has became the target of Republican fury over the illegal immigration issue.
Earlier this month, Mr Mayorkas became the first US cabinet member to be impeached over accusations from his political adversaries that he had failed to do enough to stop illegal migration.
Mr Biden has defended his colleague, who is unlikely to be convicted because the US Senate is narrowly controlled by members of his party.
Mr Trump has made the issue of illegal immigration central to his political career, and embarked on the building of a border wall with Mexico during his 2016-20 presidency.
He is only opposed by Nikki Haley in his quest to win the Republican nomination to run for the White House again. On the Democratic side, Mr Biden is largely uncontested in his own presidential bid.
Where Biden and Trump differ - and overlap - on immigration policy
The importance of the border issue has been highlighted by polling. More than two-thirds of respondents to a poll in January by the BBC's US partner CBS said they disapproved of Mr Biden's handling of it.
In another Texan border city, Laredo, the manager of a community centre described to the BBC how border agents were bussing migrants and asylum centres because they were "overwhelmed".
Far beyond Texas, the influx of illegal migrants has pushed processing facilities and social services in major American cities to the brink - straining Mr Biden's ties with some Democratic state officials.
Migrants who recently arrived in Chicago - having been sent there from Texas under the initiative of Mr Abbott - described to the BBC their struggles finding shelter and work.
Karen Diaz, who entered the US last month from Venezuela with her three young children, said she simply wanted a steady job rather than handouts.
Dilcia Guillen-Oliva, who arrived from Honduras just five days ago, said she had been sleeping in a church and on public buses as she struggled to find place in a shelter.
In a separate development on Thursday, a federal judge blocked a controversial new law planned by Mr Abbott in Texas that would criminalise illegal border crossings under the threat of jail-time.
SB4, as it is known, intends to give officials sweeping powers to arrest anyone suspected of illegally crossing from Mexico.
But in his ruling, the judge sided with the Biden administration, which argues that the planned legislation would interfere with the powers of the federal government. Mr Abbott has vowed to appeal.
