US President Donald Trump on Monday hosted El Salvador's President Nayib Bukele, who is now the US leader's key ally in a controversial push to deport illegal migrants to a notorious Salvadoran prison.

The meeting comes as the White House faces pressure over the case of Kilmar Abrego Garcia, a father who was mistakenly deported to the jail in the Central American country.

A federal judge ordered the government to "facilitate" Abrego Garcia's return to the United States, but Trump officials contend he is now solely in Salvadoran custody, leaving the man in legal limbo.

Bukele addressed the issue in his meeting with Trump, saying he would not return Abrego Garcia.

"How can I return him to the United States? It's like, I smuggle him into the United States?...I don't have the power to return him to the United States," Bukele said.

Bukele, known for his stylish dress sense and social media savvy, is broadly popular at home for clamping down on once rampant drug gangs that terrorised El Salvador.

But the 43-year-old Salvadoran leader is accused of overseeing mass human rights violations, epitomised by a huge, brutal prison known as CECOT.

Shortly after Trump's inauguration for a second term, Bukele made the extraordinary offer to take in prisoners from the United States.

Trump took the Salvadoran leader up on his proposal, sending more than 250 migrants there after invoking a rarely used wartime law dating to 1798, which stripped the deportees of due process.

Slickly produced footage of their arrival - including chained and tattooed men having their heads shaved and being frog-marched by masked guards - was widely promoted by both the Salvadoran and US governments.

The Trump administration contends that the migrants are members of criminal gangs designated by the United States as terrorist organisations, including El Salvador's MS-13 and Venezuela's Tren de Aragua.

However, relatives of several of the men contend they have no connection to organised crime and in some cases had been swept up simply because they had tattoos unrelated to any gang activity. (AFP)