Delegates to the congress said they had received messages critical of Mugabe and Vice President Joyce Mujuru.
Econet Wireless is doing all it can to distance itself from these SMSes.
Chief Executive Officer Douglas Mboweni said although the texts were sent through an Econet number they actually originated in Sweden.
He said he contacted a Swedish phone company, named Tele2 Comviq, to tell them to stop sending the messages.
Mboweni claims that millions of political messages are being sent through the Swedish platform.
He saidt international laws had been violated.
One of the messages said Mugabe should be ditched as head of Zanu-PF at the congress.
That did not happen, but these SMSes served to underline the deep divisions that still exist within the former ruling party.