The prime minister has suggested that he wants to change the law to "send away" more asylum seekers who reach the UK.
Boris Johnson called crossing the English Channel a "very bad and stupid and dangerous and criminal thing to do" amid a surge in migrant boat crossings.
He said the government wanted to "look at the legal framework that means that when people do get here, it is very, very difficult to then send them away again”.
The Ministry of Defence deployed a surveillance aircraft to the English Channel on Monday morning as attempts to reach Britain continued.
The defence secretary authorised an Atlas aircraft to be sent from RAF Brize Norton to the coast as an “initial offer of assistance” to support Border Force operations.
An official request had been made to the Royal Navy for help and a former Royal Marine has been appointed “clandestine Channel threat commander”.
The surveillance aircraft’s deployment was announced after an inflatable dinghy carrying around 20 Syrian migrants was met off the coast of Dover earlier on Monday morning.
One man could be seen bailing out water with a plastic container from the boat, which sat low in the water in choppy conditions.
More than 677 people reached the UK in a surge of crossings between Thursday and Sunday.
They added to a total of more than 4,000 migrants who have crossed the dangerous Dover Strait in small boats so far in 2020.
Speaking during a visit to a London school on Monday morning, Mr Johnson said he wanted to "send away" more asylum seekers who reach Britain on irregular routes.
The said the "problem is that there are people who want to come from around the world to this country because obviously it's a great place to be".
“Be in no doubt what's going on is the activity of cruel and criminal gangs who are risking the lives of these people taking them across the Channel," the prime minister added.
"We want to stop that working with the French, make sure that they understand that this isn't a good idea, this is a very bad and stupid and dangerous and criminal thing to do.
“But then there's a second thing we've got to do and that is to look at the legal framework that we have that means that when people do get here, it is very, very difficult to then send them away again even though blatantly they've come here illegally.”
Deportations are currently made under the Dublin regulation, which requires asylum seekers to claim asylum in the first safe country they arrive in.
Last month, the home secretary said that 166 people were already due to be returned to Italy, Germany and France, and requests had been made for another 577 migrants who arrived in Britain this year.
Priti Patel has been criticised for failing to meet a vow made last year that such crossings would be made an “infrequent phenomenon”.
Chris Philp, the immigration minister, will hold the latest round of talks with French counterparts in Paris on Tuesday in a bid to reduce numbers.
Pierre-Henri Dumont, who represents Calais in France's National Assembly, told BBC Radio 4's Today programme that local authorities were “already trying to do whatever we can”.
“If you've got dozens of crossings a day, that's very difficult for us to stop,” he added.
“It only takes five minutes to have a small boat at sea full with migrants, with a coast of 300km to monitor.”
Mr Dumont said he believed deploying Royal Navy ships “won't change anything” and called the move a “political measure”.
He warned that it would be dangerous to try to intimidate or move migrant boats, and cautioned against entering French territorial waters without permission.
Last month, the UK and France launched a new intelligence-sharing unit intended to crack down on traffickers behind migrant crossings in the English Channel.
Ms Patel and her French counterpart Gerald Darmanin stressed their “shared commitment to returning boats in the Channel to France, rather than allowing them to reach the UK”.
Hundreds of millions of pounds have been spent in the last 10 years on bilateral arrangements, including the 2019 Sandhurst treaty.
A “joint action plan” saw the UK pay £6m for increased security along the French coast, including beach patrols and drones.
At least four migrants died attempting to cross the English Channel in 2019 and a report released in November accused the government of driving people to attempt the perilous crossings.
The Foreign Affairs Committee said the UK’s focus on closing borders “serves to drive migrants to take more dangerous routes and pushes them into the hands of criminal groups”.
MPs condemned ministers for allowing “dire conditions” suffered by migrants in northern France to continue, while instead ploughing money into increased security along the French coast.
The report cited research carried out by the government itself that said crackdowns at French ports had caused an increase in small boat crossings over the English Channel.
“Focusing on increasing border security without improving conditions in the region may have the counterproductive effect of forcing migrants to make desperate journeys across the Channel,” the committee concluded.
Last week, the Home Affairs Committee launched a new inquiry to examine the reasons behind a surge in crossings since 2018.
It said MPs would look at the role of criminal gangs and “the response of UK and French authorities to combating illegal migration and supporting legal routes to asylum”.
Amid persistent warnings by refugee charities, the committee said it would investigate the conditions in camps in northern France, the risk to life during boat crossings and the response by British authorities.
Yvette Cooper, chair of the Home Affairs Committee, said: “The English Channel is one of the busiest shipping channels in the world and these crossings are incredibly dangerous. Criminal gangs are making money from putting people in flimsy dinghies and it is particularly troubling to see children being put at risk.”
Additional reporting by PA