LONDON (Reuters) - The world's leading central bank umbrella group, the Bank for International Settlements, has delivered its first public warning about the risks posed by U.S. President Donald Trump's trade war and deregulation plans.

BIS head Agustin Carstens said trade developments were a prominent worry now, while fiscal policy, regulation, immigration policy and the broader geopolitical backdrop all carry major question marks.

"Such pervasive policy uncertainty will affect central banks in several ways," Carstens, who was previously governor of the Bank of Mexico, said in a speech delivered in Mexico City.

Economic growth is likely to suffer, he said, as companies postpone investment and households put off large purchases.

Financial markets are also likely to be more volatile, given the sizeable currency and asset market swings seen in recent weeks as investors have struggled to gauge the tariff threats to Canada, Mexico and China.

"Some of these asset price movements, particularly exchange rate depreciations, could be inflationary," Carstens said, urging central banks to respond by sticking to their primary job of keeping inflation in check.

The BIS is a forum for the world's top central banks, helping to manage their foreign exchange reserves and it also hosts the Basel Committee for Banking Supervision.

Trump's re-election has threatened to shatter the already-fraying global consensus on financial rulemaking, triggering worries, especially in Europe, of a global race to the bottom in supervision.

Carstens also warned about loose fiscal policies and a possible further surge in debt, which typically fuels inflation and buffets currencies. "In the extreme," he said, "an abrupt repricing of public debt could put financial stability at risk."

There is also the danger of an amplified divergence between U.S. interest rates and those of other major economies.

"Economic growth in the United States has been much stronger than in much of the rest of the world of late," Carstens said. "Should this continue, we could see greater variability in (central bank) policy settings, with flow-on effects to capital flows, exchange rates and global financial conditions."