Downing Street has denied claims a deal was struck with Romania to relax migrant controls in return for helping Tony Blair meet asylum seeker targets.
Blair says public confidence in the asylum system must be restored
According to the Sunday Telegraph, Mr Blair promised to lift all visa requirements by spring of this year.
Downing Street said the government was working with the Romanians to remove the need for visas but denied it was a trade-off to cut asylum seeker numbers.
Mr Blair will meet ministers on Tuesday for an immigration "stock take".
Immigration Minister Beverley Hughes was forced to resign last week over the issue of Romanians and Bulgarians using forged documents to enter the UK.
Ms Hughes admitted she "unwittingly" misled people about her knowledge of a suspected visa scam, after the Tories had accused the Home Office of approving visa claims from eastern Europe, despite warnings they were backed by forged documents.
The proposed summit with Home Secretary David Blunkett and Department of Work and Pensions and Foreign Office ministers will kick-start a "cross-government assault" to tackle abuse of the immigration system, a spokeswoman said.
Security services representatives responsible for dealing with organised crime will also be there.
The spokeswoman said Mr Blair was determined not to allow abuses in the system to poison the idea of managed migration, which had brought numerous benefits to the UK.
'Rooting out abuse'
She said: "The prime minister does not accept that the immigration system is in crisis.
"However, he does believe that there has been a decline in public confidence in the integrity of the processes.
"That has to be addressed and rooting out abuse is vital."
BBC political correspondent Reeta Chakrabarti said the aggressive terminology was designed to show Mr Blair "means business over illegal immigration" and the aim of Tuesday's meeting was to make sure each department knows who is doing what.
Beverley Hughes was forced to resign over fraudulent visa issues
The spokeswoman said the prime minister believed Mr Blunkett had done "a brilliant job at the Home Office dealing with tough issues".
The Sunday Telegraph quotes an unnamed senior minister who claims the prime minister did reach an agreement to relax visa controls on Romanian migrants coming to the UK.
He says it was linked to a commitment by the Romanians - due to join the European Union in 2007 - to tackle "organised criminality" in their country.
It comes after the prime minister promised in February last year to halve the number of asylum applications within six months.
However the spokesman said: "There is no question here of a deal or trade-off. We are working very hard with the Romanian government to stop illegal immigration and to get to a point where visas are no longer necessary."
Shadow home secretary David Davis said the latest disclosures highlighted the need for a full independent inquiry.
He said: "Tony Blair was deeply involved in attempts to manipulate the figures for asylum seekers coming into this country rather than trying to resolve the problem properly."
Meanwhile an opinion poll on Saturday revealed four out of five voters believe the government is too soft on immigration policy.
The YouGov survey also found two-thirds either did not trust Mr Blair very much or did not trust him at all to bring the issue under control.