Rishi Sunak has admitted "not enough" asylum claims are being processed, but promised to fix the system.
He was responding to questions from Sir Keir Starmer who accused the government of having "lost control".
The Labour leader also called for Suella Braverman to be replaced with a "proper home secretary".
Last week MPs were told that just 4% of those coming to the UK via small boat Channel crossings in 2021 had received decisions on their asylum claims.
The government is also facing questions about severe overcrowding at the Manston asylum processing centre in Kent, which has reportedly led to outbreaks of disease and violence.
There have been reports of over 4,000 people staying at the centre, despite it being meant to hold just 1,600 when it was built.
Migrants are supposed to be kept at the centre for 24 hours only but the chief inspector of immigration has said some people had been there for over a month.
On Monday, Ms Braverman said illegal migration was "out of control" and acknowledged the system was "broken".
Repeating her comment at Prime Minister's Questions, Sir Keir asked Mr Sunak "who broke it?"
"If the asylum system is broken and his lot have been in power for 12 years - how can it be anyone's fault but theirs."
The prime minister defended his government's record, pointing to an increase of staff at Manston and the number of hotel beds available for arrivals.
"These are significant steps that demonstrate we are getting a grip of this system," he told Sir Keir.
He accused Labour of not having a plan to fix the problem, describing their policy as "a blank page".
Sir Keir said the government had wasted £140m on the Rwanda scheme which has so far failed to deport any failed asylum seekers.
He urged the government to "scrap the Rwanda gimmick, crack down on smuggling gangs, end the small boat crossings, speed up asylum claims and agree an international deal on refugees?
"Start governing for once and get a grip."
Earlier this year, the government announced plans to send some asylum seekers to Rwanda where they could claim refuge.
Ministers argue this would reduce the numbers crossing the English Channel, but the policy has been held up by legal challenges.
Almost 40,000 people have crossed the Channel in small boats so far in 2022 - the highest number since figures began to be collected in 2018.
Earlier this week, Ms Braverman describing the numbers arriving in the UK as an "invasion on the south coast".
The United Nations Human Rights Commissioner has now criticised the home secretary, saying invasion was "a horrible word".
Speaking in Geneva Volker Türk said politicians had to sure their words didn't "add fuel to the fire on issues that are about human beings".
Source: BBC
Image source: Sky News
