CAPE TOWN (Reuters) - South Africa's main prosecutor said on Friday investigations into Finance Minister Pravin Gordhan's role in setting up a surveillance unit at the tax department that allegedly spied on politicians were at an advanced stage.

The rand eased briefly against the dollar, moving to 0.76 percent down on the day 0.61 percent lower before the news, amid concerns the outcome of the probe could shake financial markets.

"The status of the rogue unit investigation - I've been advised that investigations are at an advanced stage," National Prosecuting Authority head Shaun Abrahams told a parliamentary hearing in Cape Town.

Abrahams dropped fraud charges on Monday against Gordhan, executing a U-turn in a case that had rattled markets and drawn accusations of political meddling.

He confirmed that Gordhan was still being investigated for his role in setting up the surveillance unit at the tax department a decade ago when he headed the revenue service.

Gordhan was first questioned about this in February by the police but in August ignored a follow-up summons, saying he had done nothing wrong.

Investors and credit rating agencies back Gordhan's plans to rein in government spending in an economy that has been forecast by the central bank to grow only slightly this year.

Asked if the probe on the surveillance unit would be handled in the same manner as the fraud investigation on Gordhan, Abrahams said: "Of course we will ensure that the same thing doesn't happen in this particular matter."

(Reporting by Wendell Roelf; Writing by James Macharia; Editing by Ed Cropley)