Joe Biden has accused Ron DeSantis of “playing politics with people’s lives” for flying Venezuelan migrants to the wealthy liberal island community of Martha’s Vineyard without warning, while the legality of the Florida governor’s move is also under scrutiny.

In what immigration activists and Democratic politicians have decried as a “political stunt”, DeSantis, who is expected to run for the Republican party’s presidential nomination in 2024, arranged for two charter planes of about 50 migrant adults and children to fly from Texas to Martha’s Vineyard on Wednesday.

Claiming that “every community in America should be sharing in the burdens,” DeSantis told a press briefing he wanted to draw attention to what he claimed was a failure by the Biden administration to secure the US-Mexico border.

The president attacked DeSantis’s action in a speech late on Thursday, also criticising Texas’s Republican governor, Greg Abbott.

Abbott arranged for two buses from his state to drop off more than 100 migrants from Colombia, Cuba, Guyana, Nicaragua, Panama and Venezuela at the Washington DC residence of the vice-president, Kamala Harris, on Wednesday, shortly before the Massachusetts planes landed.

The leader of the anti-trafficking charity Polaris on Friday issued a strongly-worded statement that pointedly questioned whether the governors’ actions amounted to human trafficking, citing migrants’ claims that they were deceived about where they were going.

“Acts of calculated deception were reportedly used to trick migrants onto buses and planes,” the statement from Polaris chief Catherine Chen said. “Unfortunately, this tactic is one that we know far too well in the anti-trafficking world. Migrants are regularly tricked and defrauded as part of their trafficking experience, with traffickers and exploiters taking advantage of their recent arrival, limited English proficiency, and unfamiliarity with our government systems and labor laws.”

Chen added: “If migrants were defrauded, and if this fraud was intended as a vehicle for anyone’s material gain, including that of an elected official, then there is a case for investigating it as trafficking.”

DeSantis, Abbott and Doug Ducey, governor of Arizona, have sent thousands of migrants to predominantly Democratic-run “sanctuary” states and cities they deem to be liberal over immigration, although Massachusetts has a Republican governor, Charlie Baker.

“Instead of working with us on solutions, Republicans are playing politics with human beings, using them as props,” Biden said at a gala for the Congressional Hispanic Caucus in Washington DC.

“What they’re doing is simply wrong. It’s un-American, it’s reckless and we have a process in place to manage migrants at the border. We’re working to make sure it’s safe and orderly and humane.

“Republican officials should not interfere with that process by waging these political stunts,” he added.

Veronica Escobar, a Democratic congresswoman from Texas, meanwhile, said DeSantis was “a soulless human being”.

On Friday, as Baker said he had ordered up to 125 members of the Massachusetts national guard to help move the migrants to more secure accommodation at a military base in Cape Cod on the mainland, questions were mounting over the legality of DeSantis’s action.

The US attorney for Massachusetts, Rachael Rollins, said she planned to speak with the justice department, and Nikki Fried, a member of the Florida cabinet and the only statewide-elected Democrat, wrote to the US attorney general, Merrick Garland, to demand a federal investigation into potential human trafficking.

California’s Democratic governor, Gavin Newsom, said he had also written to the justice department, which declined comment when contacted by the Guardian on Friday.

Charlie Crist, the Democratic nominee for Florida governor, who will challenge DeSantis in November’s midterm elections, said he had filed a sunshine law request demanding information about the state’s legislature-approved “relocation programme”.

Earlier this year politicians granted $12m (£10.5m) for DeSantis’s plan to relocate migrants to other states, but the language is specific to undocumented immigrants physically in Florida.

Both flights to Massachusetts touched down briefly in Florida en route between San Antonio and Martha’s Vineyard, but DeSantis’s office did not say if that was an attempt to meet the requirement of the programme.

The southern Republican governors have been transporting migrants who are, at least temporarily, legally in the US waiting for their immigration cases, such as seeking asylum from violent regimes, to be processed.

Crist in a statement accused DeSantis of trafficking humans with Florida taxpayer money. “He owes the people of our state answers,” Crist added.

In Edgartown, the Martha’s Vineyard county seat and old whaling port, on Friday, residents and aid groups were working to care for and relocate the Venezuelan families, many of whom speak no English and say they were not told of their destination when they boarded the plane.

Several told journalists there was nobody at the airport to greet them, and they walked almost four miles to find help in the town, where they were put up in a church overnight.

“They were told there was a surprise present for them, and that there would be jobs and housing awaiting for them when they arrived. This was obviously a sadistic lie,” Rachel Self, a Boston immigration attorney assisting with the migrants’ cases, said at a press briefing.

Self said she believes the migrants in question were kidnapped and defrauded, and any who cooperate with investigators may become eligible for a visa granted to crime victims.

On Friday afternoon, White House press secretary Karine Jean-Pierre accused Republican governors involved of lying to migrants, and said DeSantis did not notify Massachusetts that “migrant children, in need of food and shelter, were about to land on their doorstep”.

“These vulnerable migrants were misled about where they were headed.”

She condemned what she called Abbott and DeSantis “creating political theater [without] creating actual solution.

She noted, however, that any legal challenge would have to come from the US Justice Department rather than the White House.

Shaw Drake, senior policy counsel on border and immigration at the American Civil Liberties Union (ACLU) said the Martha’s Vineyard case has raised “particular concerns about the level of coercion and lack of informed consent”.

“The issue of consent is of core legal concern,” Drake added.

Meanwhile, NBC News reported friction between the White House and the Department of Homeland Security about how to cope with the latest rise in unauthorized border crossings.