During a five-day tour of Slovakia, the Czech Republic and Poland, Mr O'Brien will urge the three Eastern European states to improve their records on race relations.
Britain believes that many of the Roma refugees who have sought asylum over the past year have been the victims of discrimination in the countries they have fled.
But Mr O'Brien said that in almost all cases it had been decided they did not qualify for asylum under the Refugee Convention of 1951 because they had not individually been the victims of persecution.
He said: "What we cannot do is have a situation where, because there is discrimination not being tackled in other countries, people are coming over to Britain to avoid discrimination."
During his visit, Mr O'Brien will meet ministers, police chiefs and Roma groups. Home Office staff will give advice on how Britain handles its race relations. "We are dealing with our problems the same way that other countries have to deal with theirs," said Mr O'Brien, although he admitted Britain could not be "holier than though", particularly in light of the Stephen Lawrence inquiry.
The numbers of gypsy asylum-seekers are still fairly small. Only 1,200 asylum applications were made from Slovakia and the Czech Republic in the first 10 months of last year, compared with nearly 6,000 from former Yugoslavia.
But Mr O'Brien said the costs of each applicant were significant. "They claim asylum and then seek to access local authority support and the benefits system. They are then into the appeals system with lots of legal costs associated."
Britain has been encouraged by the commitments to race equality given by the new governments in both the Czech Republic and Slovakia. But Mr O'Brien said neither was likely to be allowed to join the European Union while poor race relations forced people to flee.
Anne Thomas, of the Refugee Council, who recently went on a fact-finding mission to the Czech Republic, said the Roma were the victims of "discrimination on a massive scale".Reuse content