Earlier this week Tsvangirai was reported to be battling for his life – and supporters have been urged to pray for him.
Three of his deputies are vying to lead the party in his absence, fuelling divisions within the opposition just months ahead of key elections.
Elections are due in July, the first in 38 years without Robert Mugabe as president. He was forced to resign following a military takeover last year.
Unless Tsvangirai makes a remarkable recovery, his absence could seriously weaken the opposition and hand an easy victory to Mugabe’s successor, Emmerson Mnangagwa.
A flurry of statements have been released this week, each contradicting the one before.
According to one statement, 40-year-old Nelson Chamisa, one of Morgan Tsvangirai’s three deputies, is now acting president of the Movement for Democratic Change.
That would put Chamisa in position to succeed Tsvangirai should he not recover.
Others in the party are far from happy – notably Thokozani Khupe, who says she should be acting president.
Similarly, ex-Harare mayor Elias Mudzuri, the third MDC deputy, has supporters who say that in fact it is him who should be leader.
The party’s spokesman Obert Gutu staked out Mudzuri’s claim to the acting presidency in another statement Thursday.
All this is leading to confusion, frustration – and predictions the MDC will split, as it did 13 years ago.