Some of the first people to be deported from Europe under the terms of the EU-Turkey migration deal may have been deported by mistake, the UN refugee agency has said.

Greek police “forgot” to process the asylum claims of 13 of the 202 asylum seekers sent back to Turkey on Monday, the first day the deal was put into practice, according to Vincent Cochetel, director of UNHCR’s Europe bureau.

On Tuesday, EU officials repeatedly avoided saying whether they will investigate the allegation, which threatens the legitimacy of the deportation deal.

If proved, the claims would undermine the EU’s argument that the deal, which could lead to the expulsion of almost all asylum seekers who arrived in Greece after 20 March, is in line with international law. The EU has previously promised that people “who apply for asylum in Greece will have their applications treated on a case by case basis”, and that “there will be no blanket and no automatic returns of asylum seekers”.

Cochetel said on Tuesday that 13 Afghans and Congolese asylum seekers who reached the Greek island of Chios after 20 March, and who were deported back to Turkey on Monday, had not been allowed to formally register their asylum claims due to administrative chaos on the island.

Afghans are escaping Islamist extremism and a decades-old civil war, while the eastern parts of the Democratic Republic of the Congo have been hit by a longrunning insurgency.

Cochetel told the Guardian: “For four days after the 20th, the Greek police did not register any intention to seek asylum as they were not prepared [or] equipped for this, so we started providing forms to people who had declared their intention to seek asylum.

“The police received most of the people with these forms and … forgot some apparently. It is more a mistake than anything else, we hope.”

Asked to comment on the allegations, Chios police denied that anyone had been returned to Turkey against their will. “All of the 66 people we sent yesterday did not want to stay in Greece,” said an official at Chios police headquarters, who did not give his name.

The EU commission’s chief spokesman, Margaritis Schinas, tried to laugh off the allegation, on the grounds that UNHCR had earlier said it had been given access to the deportees. Later on Tuesday, a second EU official repeatedly refused to say whether the EU would investigate the claims.

“According to our information, all those persons who were returned were aware of their rights and had the opportunity to claim asylum,” said Tove Ernst, migration spokesperson for the EU commission.

Before the deal’s creation, rights campaigners and politicians repeatedly warned that the Greek authorities needed more support to make the returns procedure work properly. The head of the Greek asylum service, Maria Stavropoulou, said on Friday her department may need a 20-fold increase in manpower to thoroughly process people’s claims.

Even Diederik Samsom, the Dutch politician who promoted the EU deal before its introduction, expressed concerns about possible mistakes. “We must ensure that all procedures are in order,” he told Dutch media during a visit to the Greek islands over the weekend. “To be honest, at the moment this is not yet the case.”

Samsom did not respond to requests for comment on Tuesday, but a coalition of 90 European refugee charities – the European Council on Refugee and Exiles – called for the deportations to be immediately suspended.

“ECRE joins the growing number of calls for an immediate halt of the transfers to Turkey,” said its secretary-general, Catherine Woollard. “It’s not only a question of capacity in Greece: the deal itself is fundamentally flawed.

“We are very concerned but not surprised to hear that asylum seekers might have been returned to Turkey ‘by mistake’. Our assessment of capacity in Greece from March showed serious gaps – and the information we have from those on the ground is that the situation has not significantly improved.”

Amnesty International’s deputy Europe director, Gauri van Gulik, travelled to Chios on Tuesday afternoon to investigate the UN’s claims. “The whole deal was ill-conceived to begin with and until there are rock-solid guarantees in practice that both sides will respect the right to seek asylum returns should stop,” Van Gulik said.

No deportations took place on Tuesday, and according to Turkish officials Greece has postponed the return of the next group from Wednesday to Friday.

More migrants are likely to try their luck in the opposite direction in the meantime. On Monday more asylum seekers landed in Greece from Turkey (228) than were deported to Turkey from Greece (202). However, the arrival rate has been reduced by about 90% over the past two months.