"They will continue to play one-day cricket as a pathway for the players," ICC president Ehsan Mani told a news conference at Lord's on Thursday.
"The dispute between the Zimbabwe Cricket Union (ZCU) and the players is a worrying issue. It should have been resolved in Zimbabwe."
Zimbabwe agreed to postpone their remaining 2004 Tests last month after the ZCU became embroiled in a dispute with 15 of the country's leading white players over team selection.
The players, angry over Heath Streak's departure as captain, made themselves unavailable for selection and were then sacked, leaving Zimbabwe with a side unable to compete at the top level.
"What we want is to protect the integrity of cricket and cricket in Zimbabwe," Mani added.
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Zimbabwe are next due to play in the ICC Champions Trophy in England in September, followed by a one-day series in Pakistan in October.
England are then due to visit Zimbabwe and are considering playing five rather than four one-dayers.
ACTIONS SCRUTINISED
The ICC, holding its annual meeting over the past four days, also announced that all spin bowlers would have their actions examined during the Champions Trophy.
Sri Lankan spinner Muttiah Muralitharan, who has pulled out of the tour of Australia, has been reported for his "doosra", or leg break delivery, and has undergone extensive testing.
Australian Prime Minister John Howard has labelled him a "chucker" and ICC chief executive Malcolm Speed reacted sternly to the remarks.
"It is great to see prime ministers all over the world interested in cricket but cricket would have been better served if Howard had not made that comment," he said.
The governing body is based in a tiny building on the Lord's complex and has been searching for a new home outside a member country.
Dubai and Malaysia had been favourites for the relocation but the British government has now submitted a late proposal for the ICC to stay in London and the decision has been deferred.
Speed was pleased by the possible intervention but said: "We are disappointed it came at the 59th minute of the 11th hour. But there is a strong possiblity we would have relocated from London. The tax issue is a very big issue."