The UK Government has dismissed the first minister's call for Scotland to be given special treatment on the issue of the removal of asylum seekers.
The Vucaj family, who were deported after a dawn raid
Immigration Minister Tony McNulty said no concessions could be made for Scotland, despite the Scottish Executive's unease at the system.
Jack McConnell had hoped that the executive would be consulted before failed asylum seekers were removed.
He has been attacked by political opponents over the snub.
Mr McNulty said there could not be different arrangements around the UK.
Mr McConnell has repeatedly called for Scotland to be made a special case in relation to asylum, particularly over the use of dawn raids to remove families from their homes.
Campaigners have increased their efforts to stop such raids following the deportation of the Vucaj family from their home in Glasgow.
Scottish Socialist Party MSP Tommy Sheridan was among those who targeted the immigration service office in Govan, Glasgow, resulting in his arrest on Monday.
The 41-year-old appeared at Glasgow Sheriff Court on Tuesday charged with breach of the peace.
He was granted bail on condition that he does not approach the Immigration Centre in the future.
Mr McConnell's Fresh Talent initiative is aimed at helping to attract skills to Scotland and reverse the declining population. Educated asylum seekers are seen as offering some of the skills which are in short supply in Scotland.
Last week, the Scottish Parliament's external relations committee urged the Scottish Executive to lobby the Home Office over rules which prevented employment asylum seekers from taking up jobs.
Mr McNulty will be in Scotland on Thursday to meet Scottish Executive officials and organisations involved with asylum seekers.
Ahead of his visit, it has emerged that he will tell Mr McConnell there can be no special arrangements with the executive on the issue of dawn raids.
BBC Scotland home affairs correspondent Reevel Alderson said educational or medical criteria would be taken into consideration but he pointed out that that was already happening across the UK and was not a concession to the executive.
Fresh Talent is an executive drive to bring in new skills
Mr McNulty said: "We have had a series of constructive discussions with the Scottish Executive about involving social work and education services in advance of removing failed asylum seekers where children are involved.
"Those discussions are ongoing. As we have always made clear, any changes we may make would be UK-wide.
"The home secretary has made this clear in discussions with the first minister."
Scottish Conservative leader Annabel Goldie said: "What today's development shows loud and clear is that the first minister has no status, no stature and no authority with his colleagues in Westminster.
"I am calling for the first minister to come before the parliament and to make a statement at the earliest possible opportunity in order to clarify what the actual situation is."
SNP Holyrood leader Nicola Sturgeon said: "It now appears that the first minister is at best muddled over the Home Office's position.
"We need to know if the first minister was misinformed or if he misled parliament."
The Scottish Green Party's justice spokesman Patrick Harvie said: "Jack McConnell is looking increasingly foolish on this issue. He must come clean on this, and quickly.
"McConnell's stock with Labour colleagues in London must be very low. Now we can see just how powerless he is."