Vice-President Kamala Harris has faced pressure to visit the US-Mexico border, as she tries to tackle a record migration spike.
Ms Harris had a testy exchange with a journalist who asked why she had not gone to the US southern boundary.
Members of Ms Harris's own Democratic party meanwhile criticised her after she warned against illegal immigration.
On a visit to Mexico on Tuesday, she said Washington aimed to boost economic development in the region.
She and Mexican President Andrés Manuel López Obrador said it was in the interests of both countries to address the root causes of migration.
About 178,000 undocumented migrants arrived at the US southern border this April, the highest total in more than two decades.
The vice-president's staff initially said the border was part of Ms Harris's portfolio when US President Joe Biden assigned her in March to stem migration from Latin America. But aides have recently been seeking to distance her from the politically toxic crisis.
While recent public polling suggests a generally favourable view of the Biden administration's policies on the economy and pandemic, its handling of the immigration crisis has proven less popular.
Asked in an interview with NBC News aired on Tuesday morning whether she had any plans to visit the border, Ms Harris threw up her arms and responded: "At some point. You know... we are going to the border. We have been to the border."
When the host pointed out that she had not herself visited the region, she said with a laugh: "And I haven't been to Europe. I don't understand the point you're making."
Ms Harris again brushed off questions about why she had not gone to the border as she spoke to reporters on Tuesday in Mexico.
"It would be very easy to say," she said, "we'll travel to one place and therefore it's solved. I don't think anybody thinks that that would be the solution."
Pressed on why she would not visit the border, Ms Harris said she had done so when she was a senator for California.
Ms Harris's remarks came at the end of a two-day visit to Guatemala and Mexico, where she met both countries' leaders in a bid to bolster diplomatic ties and help stem undocumented migration to the US.
Capping off her trip on Tuesday, Ms Harris met President López Obrador privately for more than an hour, said the vice-president's aides.
It is unclear whether she pushed Mexico's president to do more to detain migrants en route to the US. Mr López Obrador, a left-wing leader, has previously blamed the Biden administration for causing the record surge in undocumented migration.
An aide to Ms Harris later said she had pledged $130m (£92m) in US aid to support Mexican workers' rights. She has already promised $310m to alleviate the impact of the pandemic and hurricanes last year in Central America.
Back at the White House daily briefing on Tuesday, Biden spokeswoman Jen Psaki was asked why Ms Harris had not visited the US-Mexico boundary.
"I think that at some point she may go to the border," Ms Psaki said. "We'll see."
Kamala Harris's inconsistent message
For as much as she may be coming under pressure to visit the border back at home, it's what she said earlier on this trip which is causing dismay in Central America. Specifically her stark warning that would-be migrants "do not come" - three words she repeated for added emphasis.
A wide array of activists, human rights lawyers and journalists have pointed out the inconsistency in such a message. First, they say, it fails to take into account the reality on the ground for so many millions of the poorest in Central America. Battered by hurricanes, hunger, natural disaster, climate change and coronavirus, the economic downturn in the region could last for many years. That's to mention nothing of the rampant gang violence and forced recruitment of vulnerable young people in the region.
Added to that, her statement appeared to ignore the fact that requesting asylum is a legal right, one which Ms Harris had berated the Trump administration for undermining while she was a candidate. More than one observer has commented on how it was particularly jarring to hear it from the vice-president, as the daughter of immigrants herself.
In Mexico, the focus shifted to broader bilateral issues: the economy, security co-operation, development plans for southern Mexico and Central America. Yet immigration remains the overriding concern for the Biden administration in this part of the world. For as much as both countries spoke at length of "orderly, safe and regular migration flows" or tackling the "root causes of migration", most people will remember Vice-President Harris's first international trip for those three short words: "Do not come".
Why are fellow Democrats criticising Harris?
Critics across the political spectrum said Ms Harris's remarks in Guatemala on Monday contradicted the Biden administration's promise to usher in a more humane approach on migration.
"Do not come. Do not come," the vice-president warned illegal immigrants, adding: "If you come to our border, you will be turned back."
While running for the presidency in 2019, Ms Harris lambasted then-President Donald Trump for turning away undocumented immigrants at the border.
"What does Donald Trump do?" she said. "He says, 'go back where you came from.' That is not reflective of our America and our values and it's got to end."
Ms Harris's remarks on Monday provided fodder for her regular Republican critics, but they also provoked rare rebukes from left-wing members of her own party.
Alexandria Ocasio-Cortez, the influential New York City Democratic congresswoman, called the remark "disappointing".
"First, seeking asylum at any US border is a 100% legal method of arrival," she tweeted.
"Second, the US spent decades contributing to regime change and destabilisation in Latin America. We can't help set someone's house on fire and then blame them for fleeing."
Fellow members of her ultraliberal group known as the Squad also criticised Ms Harris, who is herself the daughter of migrants - an Indian-born mother and a Jamaican-born father.
"The right to seek asylum is not just legally protected. It is a foundational universal human right," tweeted Minnesota congresswoman Ilhan Omar, who was born in Somalia.
Michigan's Rashida Tlaib also hit out at Ms Harris, writing: "This whole 'stay there and die' approach is not how our country will promote a more humane and just immigration system."
Asked later about the criticism, Ms Harris said: "I'm really clear. We have to deal with the root causes and that is my hope. Period."