Despite the two-week ceasefire in the conflict in Iran, much damage has already been done to Europe's economy, with S&P Global reporting a dented growth across the eurozone, and a European Central Bank policymaker saying interest rates may need to be hiked.

Dimitar Radev, a member of the ECB's governing council, said the bank will have to raise interest rates quickly if there are signs of persistent price pressures.

He told Reuters that surging energy costs caused by the conflict have already pushed inflation past the bank's 2 percent target and triggered discussions about rate hikes.

"The balance of risks has shifted in an unfavorable direction," he said.

Radev, who is also head of Bulgaria's central bank, said "the likelihood of a more adverse scenario (for the economy) has increased, particularly in light of the energy shock and the elevated level of uncertainty".

The ECB is worried that businesses and consumers could become accustomed to high energy prices and bake them into their expectations, with businesses subsequently charging more for products, and consumers demanding higher wages, he said. That could set off an inflationary spiral that would be costly to control, he added.

The warning came as the latest numbers from S&P Global's Composite Purchasing Managers' Index show the eurozone's private sector expansion weakened sharply in March, because of the impact of the Iran conflict on energy prices and disruption to supply chains and demand.

The first fall in the index in eight months put the eurozone's PMI at 50.7 in March after it had been 51.9 in February. PMI readings above 50 indicate growth.

"March's PMI indicates that the eurozone economy has already been hit hard by the war in the Middle East," said Chris Williamson, chief business economist at S&P Global Market Intelligence.

The figures show new business declined in March because of a lack of demand, and overall export orders fell. Additionally, employment levels fell, and business confidence dropped.

Among eurozone nations, Spain had the strongest growth. France and Italy contracted. And Germany's expansion slowed to a crawl.

Headline inflation in the eurozone is now running at 2.5 percent, up from 1.9 percent previously.