World cricket's governing body will encourage top countries to keep playing against Zimbabwe after it withdrew from the Test arena for the next 12 months.
But it is unclear whether teams are still contractually obliged to play one-day internationals against them.
Discussions are ongoing between the ICC and officials from West Indies, where Zimbabwe are due to tour in April.
"Zimbabwe Cricket has taken a sensible step in withdrawing from its Test commitments," said ICC head Ehsan Mani.
"The Zimbabwe team has demonstrated in recent series that it is not in a position to be competitive in Test cricket.
"Its decision to withdraw from its commitments over the next 12 months helps protect the integrity of the international game."
Under the ICC's future tours programme, Zimbabwe were due to play Tests and one-day games against South Africa at home in August before touring Pakistan.
And the Pakistan Cricket Board will discuss possible compensation with the ICC.
"We have contractual obligations with our television broadcasters and they have sold bundled sponsorship rights for a four-year period," said a spokesman.
"We want to know from the ICC, if there are financial liabilities on us, who will fulfil them."
Mani hopes Zimbabwe will continue to play the longer first-class format of the game as well as limited-overs internationals.
"We will closely monitor the performance and progress of the team," he added.
"Towards the end of the year we will work with Zimbabwe Cricket to determine the most appropriate course of action."
Zimbabwe's decision followed a meeting between the ICC and the chairman of Zimbabwe Cricket's interim committee, Peter Chingoka, in Karachi last week.
ZC decided to suspend playing in Tests "after considering recent performances".
A statement said: "ZC is now putting in place a programme to galvanise the development of the Zimbabwe squads.
"It will work with other Test nations and the International Cricket Council itself to realise this objective."