Rishi Sunak admitted he does not have a date for when he will meet his pledge to “stop the boats”.
Quizzed by parliament’s most powerful committee, he insisted numbers have fallen under his premiership.
Asked what date illegal crossings will end, he replied: “The first thing to say is we have made progress. The numbers this year are down by a third, which is considerable progress.
“They are, for the first ever time, down. There isn’t a firm date on this because I have always been clear from the beginning.
“We will keep going until we do. This is not one of these things where there is a precise date on it.”
“This is something where before I took this job they had only ever gone up and now they are down by a third.”
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Mr Sunak vowed to get deportation flights in the air to Rwanda “as soon as possible”.
Legislation to curb the power of courts to block the plan is facing a rocky passage through parliament first as rebels on both wings of the Tories threaten to block it.
The PM saw off a potential revolt last week despite pressure from hardliners to pull the bill over fears it is too soft.
Mr Sunak wants to send the first flights to the East African nation in spring.
He hopes the Safety of Rwanda Bill will revive the stalled plan by blocking legal challenges made on the claim that the nation is unsafe.
It would allow ministers to disapply the Human Rights Act but does not go as far as overriding the European Convention on Human Rights.
Mr Sunak dismissed claims that no airline is willing to do a deal with the government to provide the flights over fears it will damage their commercial reputation.
He said: “I’m confident we will have the ability to send people to Rwanda.”
Appearing before the Commons Liaison committee, the Prime Minister also said there is still time to meet his target to clear the legacy asylum backlog of 92,000 cases by the end of the month.
He said it has already fallen by 80 per cent and “very good progress” is being made.
