Jan 2 (Reuters) - Manufacturing slumps in Poland and the Czech Republic eased slightly in December although activity remained deep in negative territory, with high prices cutting demand and firms reducing staff in response, surveys showed on Monday.

S&P Global's Polish Manufacturing Purchasing Managers' Index (PMI) rose to 45.6 in December from 43.4 in November, staying well below the 50 mark separating growth from contraction.

The headline Czech S&P Global PMI reading edged up to 42.6 in December, from 41.6 in November, with the rate of decline easing for the first time in 2022.

Hungary's seasonally-adjusted PMI, published by the Association of Logistics, Purchasing and Inventory Management (MLBKT), jumped to 63.1 in December from a revised 56.0 in November, remaining an outlier in the region.

But Hungary, like other economies in central Europe, is fighting to stay out of recession after it posted its first quarterly contraction in more than two years in the third quarter as high inflation takes a toll on the region.

The impact of high inflation - which soared to double-digit rates last year - was on display in the latest PMI readings, with Czech and Polish output and orders falling sharply.

In both countries, firms reacted by reducing workforce, the surveys found.

"Poland's manufacturing sector remained deep inside contraction territory in December to end the year in recession," said Paul Smith, Economics Director at S&P Global Market Intelligence.

"However, there were some positive signs... Rates of contraction have generally eased, and whilst a long way to go still, the sector is slowly making its way back towards stability." (Reporting by Jason Hovet in Prague Editing by Mark Potter)