Czech authorities on Tuesday sent the first patient abroad for treatment in Poland as facilities struggled to cope.
In Hungary, meanwhile, the number of cases in the current wave has surpassed the previous peak in December.
Schools and most shops were closed on Monday amid rising infections.
Cases are also on the rise in Poland, where the government recorded the highest number of daily cases since late November on Wednesday, with 17,260 new infections. A health ministry spokesman complained of "increased looseness" among Poles towards anti-Covid measures.
Restrictions were relaxed last month but they have since been re-imposed in two areas in the north.
The number of Czech patients treated in hospital with Covid-19 reached 8,618 on Wednesday, with 1,853 in intensive care. On Tuesday, the first Czech MP succumbed to the virus. Jiri Ventruba, 71, was a renowned paediatric neurosurgeon.