Tory immigration plans lack credibility and would lead to border controls being surrendered, the government said as it prepared to unveil its own proposals.
Mr Clarke is expected to make an announcement on Monday
The Tories had not said how they would pay for more immigration officers while cutting the budget, Des Browne said.
And the immigration minister said the government would launch a "test" for would-be economic migrants on Monday.
The Lib Dems said they would look at Labour's plans, but Tory Liam Fox said Labour was "rattled" on the issue.
On Monday, Home Secretary Charles Clarke will promise more removals of failed asylum seekers, a points system for economic migrants and electronic embarkation controls.
But he will rule out setting limits for those seeking refuge rather than work.
Conservative leader Michael Howard has outlined plans to set an annual limit on the number of asylum seekers allowed into the UK and that all claims should be processed abroad.
On Saturday, Labour published a document attacking Tory spending plans for asylum, immigration and policing.
Mr Browne claimed there was a "lack of credibility at the heart of Tory spending plans".
"In addition to silence on the huge cuts they plan they have added new spending commitments on asylum and immigration but have said nothing about how these would be paid for," he said.
He said the Conservatives have committed themselves to cutting nearly £900m from the asylum and immigration budget.
Mr Browne went on: "Savings of this scale could only be achieved, for example, by removing our border controls, ending our enforcement action and getting rid of our detention centres.
"The Tories have a choice, they can either make damaging cuts to our border controls or they must break their promise on police numbers."
Liberal Democrat home affairs spokesman Mark Oaten said his party would "look seriously at supporting the government's plans for quotas for economic immigration provided it is based on an independent assessment with input from both the public and private sectors."
But Conservative co-chairman Liam Fox said that since Labour came to office "immigration had trebled to 150,000 a year", adding: "That's a city the size of Peterborough arriving in the UK every year".
"It seems a little odd that this government is willing to commit British troops to Iraq in the battle against terror but is unwilling to put people manning security at our ports 24 hours a day," he added.
Mr Howard has said Britain should take its fair share of the world's "genuine refugees".
But he claims the current asylum system is being abused - and with it Britain's generosity.
The Refugee Council said Mr Howard's proposals would mean there would be no safe haven in the UK.
And Keith Best, chief executive of the Immigration Advisory Service, said: "The government and opposition seem determined to play to the lowest and most ignorant attitudes of some sections of society by promising greater control when it is largely illusory."