WARSAW, July 1 (Reuters) - Hungary's manufacturing sector tipped into a downturn in June, a survey showed on Monday, while Polish and Czech manufacturers remained mired in a slump as poor demand weighed on orders and output.

Hungary's purchasing manager's index (PMI) fell to 49.4 in June compared to a revised reading of 51.3 in May, falling below the 50.0 mark that separates growth from contraction for the first time since January. The index is published by the country's Association of Logistics, Purchasing and Inventory Management (MLBKT).

Peter Virovacz, senior economist at ING in Hungary, said that industrial production data showed that the sector had already been in a downturn but that this had not been reflected in the PMI.

"It is not necessarily showing that we have reached some turning point because we were in a downturn already," he said.

In Poland, S&P Global's Purchasing Managers' Index (PMI) showed the manufacturing sector contracted for the 26th month in a row, the longest sequence since the survey began in 1998.

The Polish reading remained at 45.0 for a second straight month, well below the 50.00 line that separates growth from contraction.

"It is difficult to see optimism in the incoming PMI data for the Polish industry," said Monika Kurtek, chief economist at Bank Pocztowy.

"This data indicates that the economic growth rate in the second half may be slower than previously expected, which will ultimately translate into a lower full-year result."

In the Czech Republic, S&P Global's PMI was 45.3, down from 46.1 in May.

"The persistently weak activity in the domestic manufacturing industry fits into the context of weak demand in key export markets," said Radomir Jac, chief economist at Generali Investments CEE.

"I still expect the situation to improve in the second half of this year... However, the June survey suggests that the process of recovery of activity in the domestic manufacturing industry may be very gradual." (Reporting by Alan Charlish, Anita Komuves in Budapest, Jan Lopatka in Prague; Editing by Emelia Sithole-Matarise)