While South Africa has a fine Constitution, its handling of illegal migrants is not up to par, MPs heard on Monday.

United Nation Special Rapporteur on Human Rights, Jorge Bustamante, told members of Parliament's home affairs portfolio committee there was a "general lack of data" when it came to the human rights of migrants.

"The fact that there are so many undocumented immigrants in South Africa already, makes South Africa behind the realities of international migration. And that is something that is very much in contrast with the fine, exemplary level of the Constitution of South Africa."

Bustamante said this was particularly the case with regard to the labour rights of those "that are coming... undocumented to SA, that are not dealt with with the corresponding international standards".

He said the fact that so many migrants were crossing South Africa's borders to find work indicated there was a demand for their labour.

"That is a fact... of economic dynamics."

Bustamante is on a fact-finding mission to South Africa, at the invitation of government. He arrived on January 24. His visit ends on Tuesday.

He will present a final report on his findings to the UN's Human Rights Council in June this year.

Bustamante urged MPs to recognise and measure the scale of undocumented migrant labour in South Africa.

"This is one recommendation I would make for the present circumstances that point to an increasing need for the measurement of that phenomenon of undocumented immigration that SA has on the rise.

"To be myopic about the existence of that phenomenon would lead to problems such as those... that SA had two years ago, that caught the attention of the world," he said, referring to the xenophobic violence that gripped parts of the country in 2008.