By Lucia Mutikani and Jonathan Cable

WASHINGTON/LONDON (Reuters) -U.S. manufacturing grew steadily in August but factory activity in China, the euro zone and Britain fell as Russia's war in Ukraine and China's zero COVID-19 curbs continued to hurt businesses, surveys showed on Thursday, although there were indications cost pressures were starting to ease.

The overall weakness in global manufacturing activity added to signs sluggish demand in many countries was adding to headaches for companies already suffering from lingering supply constraints.

Major central banks are expected to continue aggressive interest rate hikes in order to tame inflation, which is also dampening optimism through growing fears of a global downturn.

The Institute for Supply Management (ISM) said on Thursday that its index of U.S. factory activity was unchanged at 52.8 last month, although that is still the lowest reading since June 2020, when the sector was pulling out of a COVID-19 induced slump. A reading above 50 indicates expansion in manufacturing, which accounts for 11.9% of the U.S. economy.

But the forward-looking new orders sub-index rebounded to 51.3 last month from a reading of 48.0 in July, ending two straight monthly decreases, and order backlogs rose, suggesting factories in the world's largest economy will continue humming for a while.

U.S. manufacturing is showing resilience despite a shift in spending back to services as well as an ebb in business confidence amid rapidly rising interest rates.

There was also some relief for U.S. factories struggling with surging costs as weakening global demand is having the side-effect of easing price pressures. A measure of input prices paid by manufacturers dropped to 52.5, the lowest reading since June 2020, from 60.0 in July.

Elsewhere, input prices fell in China and Taiwan for the first time since May 2020. South Korean manufacturers saw input prices rise in August by the slowest rate in 19 months, and average input costs faced by Taiwanese goods producers fell for the first time since May 2020.

In the euro zone the input prices index remained well above its long-term average but did fall to its lowest reading since the start of last year.

However, that did little to diminish concerns about slowing global growth.

"We are forecasting a recession in the euro zone and one in the United States next year. Whether that extends into a global recession remains to be seen," said Peter Schaffrik at the Royal Bank of Canada.

MANUFACTURING SHRINKS IN EUROPE, ASIA

Outside the United States, signs of strain deepened. Manufacturing activity across the euro zone shrank for a second month in August, while weak demand meant factories were unable to sell as much as they made and built up stocks of finished goods at a record pace. [EUR/PMIM]