The White House strongly criticised the US supreme court on Tuesday for allowing what it called a “harmful and unconstitutional” Texas immigration law to go into effect.

The law, Senate Bill 4 (SB4), allows state authorities to arrest, process and imprison people suspected of crossing the US-Mexico border illegally – thereby infringing on roles long reserved for federal authorities.

The White House press secretary, Karine Jean-Pierre, said: “We fundamentally disagree with the supreme court’s order allowing Texas’s harmful and unconstitutional law to go into effect. SB4 will not only make communities in Texas less safe, it will also burden law enforcement and sow chaos and confusion at our southern border.”

At the court, the rightwing majority did not explain its reasoning for allowing the Texas law to go into effect. In a dissent, the liberal justices Sonia Sotomayor and Ketanji Brown Jackson said their rightwing colleagues had invited “further chaos and crisis in immigration enforcement”.

“Texas passed a law that directly regulates the entry and removal of non-citizens and explicitly instructs its state courts to disregard any ongoing federal immigration proceedings,” said the dissent, written by Sotomayor. “That law upends the federal-state balance of power that has existed for over a century, in which the national government has had exclusive authority over entry and removal of non-citizens.”

Underlining the significance of the decision, Sotomayor said a lower court had “declared that Texas’s law amounts to ‘nullification of federal law and authority – a notion that is antithetical to the constitution and has been unequivocally rejected by the federal courts since the civil war’.”

The third liberal on the court, Elena Kagan, issued her own short dissent in which she said the Biden administration met requirements for imposing a stay it requested, to stop SB4 while a federal challenge proceeds in lower courts.

The Texas governor, Greg Abbott, signed SB4 in December, authorising state officers to arrest people suspected of entering the US without documentation. Abbott said the law was needed due to the failure to enforce federal laws. Joe “Biden’s deliberate inaction has left Texas to fend for itself,” he said.

Border issues, including record numbers of undocumented migrants, are a key electoral issue for Republicans. Abbott and others have said Biden should have kept restrictive policies introduced by Donald Trump, the former president now the presumptive Republican nominee to face Biden in November.

House Republicans impeached Biden’s secretary of homeland security, Alejandro Mayorkas: a political move unlikely to lead to his removal, given Democratic control of the Senate.

The Biden administration points to how Republicans last month scuttled a bipartisan Senate deal that would have tightened border security and immigration laws. Biden has said blame lies with Republicans who bowed to pressure from Trump, who wants to campaign against a backdrop of supposed border chaos.

On Tuesday, Jean-Pierre said: “SB4 is just another example of Republican officials politicising the border while blocking real solutions. We remained focused on delivering the significant policy changes and resources we need to secure the border – that is why we continue to call on congressional Republicans to pass the bipartisan border security agreement, the toughest and fairest set of border reforms in decades.”

Texas has pursued other hardline measures to deter migrants, including deploying national guard troops and installing concertina wire and a floating barrier. SB4 makes undocumented entry or re-entry a crime. State judges will be required to order migrants to return to Mexico, with sentences of up to 20 years if they refuse.

In January, the US justice department sued to block the law, which was set to take effect on 5 March. Lawyers argued that the law violates federal law and constitutional provisions giving the federal government the power to regulate commerce with foreign countries and among states, and that it runs afoul of a 2012 supreme court precedent.

That year, the court struck down parts of an Arizona law that would have allowed police to arrest people for federal immigration violations and was referred to by opponents as a “show me your papers” bill, given the leeway it gave officers to determine who they approached. Then, a divided supreme court found that an impasse in Washington over immigration did not justify state intrusion.

This year, on 29 February, a Texas US district judge, David Ezra, preliminarily blocked SB4, saying it “threatens the fundamental notion that the United States must regulate immigration with one voice”. Ezra’s ruling was paused by the fifth US circuit court of appeals, a court noted for its rightwing slant. That would have let the Texas law take effect on 10 March, prompting the administration to file an emergency supreme court request.

Samuel Alito, the rightwing justice who handles emergency matters from states including Texas, temporarily halted the fifth circuit ruling.

In her dissent, Sotomayor stressed that “the only court to consider the law concluded that it is likely unconstitutional”. She also said the Texas law “implicates serious issues subject to ongoing political debate”.

Dan Patrick, the lieutenant governor of Texas, saluted a “historic” decision on a law he said he co-wrote “to give Texas the right to arrest, prosecute, and return anyone who enters Texas illegally”. He also claimed Texas was being “invaded by land, sea, and air”.

Gilberto Hinojosa, chair of the Texas Democratic party, countered that SB4 “isn’t about community safety – it’s about enabling [law enforcement] to target neighbourhoods and imprison people for the sake of Fox News headlines. This inhumane border strategy will now force American citizens to carry passports in their own neighbourhoods and enforce mass deportations of migrant women and children – all while overburdening local law enforcement.”

Sawyer Hackett, an adviser to Julián Castro – a former mayor of San Antonio and candidate for the Democratic presidential nomination – lamented an “incredible” in favour of a “blatantly unconstitutional ‘show me your papers’ law.

“The supreme court just put a target on the back of every brown person in Texas,” he said.

Mexico’s foreign ministry said later on Tuesday that it rejects what it called the Texas “anti-migrant” law aimed at stopping migration flows via “criminalization”, and also that Mexico would not cooperate with the Texas state authorities to accept people the state attempted to deport back across the border.

Reuters contributed to this report