Indian businessman Pankaj Oswal and his wife Radhika have been ordered to pay $1.2 million to the Federal Court as security to cover costs incurred by the Australian Tax Office.

The couple are in a battle with the tax office over a taxation assessment from February 2011.

Their appeal against the assessment relates to a capital gains tax event, linked to shares Mr Oswal held in Burrup Holdings Pty Ltd in the 2007 financial year.

Mr and Mrs Oswal's counsel argued the $1.2 million security payment was unnecessary because the couple's assets in Australia exceed their tax debt, but Federal Court Judge John Nicholas did not accept that.

Judge Nicholas said because of mortgages and other factors, it was difficult to ascertain the value of their Australian assets.

He also noted the pair now lived in Dubai.

Judge Nicholas gave them 28 days to hand-over the money.

In a separate matter, the couple recently agreed to demolish their unfinished mansion in Peppermint Grove after a lengthy battle with the local council.