The foreign secretary, Jeremy Hunt, has backed Sajid Javid after the home secretary was criticised for questioning whether people crossing the Channel in small boats were “genuine” asylum seekers.

Speaking in Malaysia, Hunt said: “I think the home secretary is right to say that as a country that is very proud of our tradition of granting asylum to people who need it, we also want to make sure that isn’t abused.

“But our priority right now is the safety of people in the Channel: to discourage people from making this very dangerous crossing but to make sure that everyone that does is kept safe.”

Hunt said the problem had to be “tackled at source” through international development programmes to remove the drive for people to make the dangerous crossings.

The National Crime Agency (NCA) said two men were arrested in Greater Manchester on Wednesday on suspicion of arranging the illegal movement of people into the UK. One, a 33-year-old Iranian national, was arrested in Broughton, Salford, the other, a 24-year-old British national, in nearby Pendleton.

Both men were held in custody overnight and are to be questioned by NCA detectives on Thursday.

The agency, which is investigating people smuggling as part of its work on serious organised crime, said the men were being held “on suspicion of arranging the illegal movement of migrants across the English Channel into the UK”.

An NCA spokeswoman confirmed on Thursday that the arrests were in relation to “alleged offences committed in December 2018”.

Javid cut short his holiday in South Africa to respond to the increasing number of people undertaking the dangerous journey across the Channel, and he described it as a “major incident”.

He has since requested the help of the navy to patrol the Channel. This week he announced the redeployment of two UK Border Force cutters from the Mediterranean.

A total of 539 people attempted to travel to the UK on small boats in 2018, according to the Home Office, 80% of them (434) in the last three months of the year. Overall, 227 (42%) were intercepted by French authorities before they made it to the UK.

On Wednesday Javid had suggested that people picked up by UK authorities could have their asylum requests denied to deter others from undertaking the same dangerous journey.

He was criticised for questioning whether those crossing the Channel were genuine asylum seekers. Speaking on a visit to Dover, Javid said: “A question has to be asked: if you are a genuine asylum seeker, why have you not sought asylum in the first safe country you arrived in?”

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He was also criticised for repeatedly referring to them as “illegal” migrants, even though it is not against the law to seek asylum. The Labour MP Stella Creasy, who has visited refugee camps in Calais, accused Javid of normalising “anti-refugee rhetoric”.

She said: “The asylum system in France is completely deadlocked and I fear deliberately so – they should be challenged on that. But none of that means Britain can absolve itself of responsibility to refugees. People will continue to die and be at mercy of traffickers all the time politicians pretend to play tough for votes rather than recognise why people flee.”

Paul Hook, head of campaigns at the charity Refugee Action, said: “The home secretary must remember that these are people who have fled their homes and they each deserve a decent, humanitarian and understanding response. This situation demands our compassion and cool, calm heads and we hope the home secretary will reflect this in his statements on the subject.”