As a border crisis is building, President Joe Biden is appealing to people to not come to the US, dispelling the impression for some from the campaign rhetoric that immigration restrictions would be dismantled.

"Don't come over," he said on Tuesday, repeating a plea by officials to people from Central America converging along the border with Mexico.

"Don't leave your town or city or community," he said in an interview on ABC TV.

Homeland Security Secretary Alejandro Mayorkas assured a House of Representatives Committee on Wednesday, "Border is secure, it is not open."

While White House spokesperson Jen Psaki has denied that there was a "crisis" at the border, Mayorkas said: "The Department is responding to historic and unprecedented challenges at the border, including the arrival of record levels of unaccompanied children."

Earlier he had warned: "We are on pace to encounter more individuals on the southwest border than we have in the last 20 years."

US border security personnel caught more than 97,000 people illegally crossing into the US.

"The idea that Joe Biden said, 'Come' — because I heard the other day that they're coming because they know I'm a nice guy. Here's the deal: They're not," Biden said in the interview.

In one of his manifestos, he had said: "It is a moral failing and a national shame when a father and his baby daughter drown seeking our shores" and added there would be a "humane" immigration policy.

He promised to give legal status with eventual citizenship for an estimated 11 million illegal immigrants in the country.

But his manifesto also said that he would enforce the laws on immigration and border security.

Biden is also facing criticism from his party's left for not being liberal enough.

Democrat member of the House Alexandria Ocasio-Cortez tweeted: "DHS (Department of Homeland Security) shouldn't exist, agencies should be reorganised, ICE (Immigration and Customs Enforcement) gotta go, ban for-profit detention, create climate refugee status & more".

Republicans are savouring the crisis in the hope that it would become an issue in the midterm elections next year.

Kevin McCarthy, the Republican leader in the House of Representatives, said after a visit to the border areas earlier this week that situation was a "heartbreak".

"This crisis is created by the presidential policies of this new administration. There's no other way to claim it than a Biden border crisis," he said.

Politico quoted Democrat Representative Vicente Gonzalez from a border area in Texas as saying: "Our party should be concerned", adding, "Biden is going to be dealing with a minority in Congress if he continues down some of these paths".

Biden's administration has upheld an executive order imposed by former President Donald Trump to send back immediately to Mexico those entering the country illegally and make them wait there for asylum hearings.

Trump based his order on the Covid-19 pandemic as a measure to prevent its spread.

Biden has also not lifted Trump's restrictions on asylum seekers.

However, Biden's administration allows unaccompanied children and families with children under six years into the country.

The crisis is most visible among children estimated to number about 4,000, who are straining the system.

Biden had said in his manifesto, "When children are locked away in overcrowded detention centres and the government seeks to keep them there indefinitely."

The Democrats and the media had denounced Trump for the harsh conditions in which children were being held but that appears to be recurring.

Neha Desai, an Indian American lawyer authorised by a court to monitor the conditions under which children are detained by immigration officials, told CBS TV that some of them said they were hungry, "they had to take turns sleeping on the floor" and the only time they could see the sun was when they were allowed to take showers, sometimes only once every seven days.

Ocasio-Cortez tweeted about the condition of the children in custody: "This is not okay, never has been okay, never will be okay – no matter the administration or party."

Democrats have blamed Trump for the border situation because, they said, he had dismantled the earlier system for dealing with migration.

The "fairness and efficiency in our immigration system", Mayorkas said, "was systematically dismantled during the last four years".