They are the only political party to propose at the May 1 National Assembly election a change to the policy adopted throughout Wales since 1993.
Schools would still have to offer the subject.
The move comes amid questions about the value of compulsory Welsh.
It follows evidence to the Assembly's education committee from pupils who said they were unable to speak the language fluently despite years of study.
The pupils did not advocate abandoning Welsh but they argued that it should be better taught, perhaps more selectively.
The Conservative's change of policy has been driven from Gwent, which has virtually no native-speakers and where Welsh was rarely taught at school.
Meirion Jones, from the Welsh Language Board, said the policy needed reviewing but accused the Conservatives of jumping the gun.
The director of language planning said: "We have to await the first cohort of pupils to pass through Gwent schools, where the policy was not adopted until 1993."
A review would focus on issues such as funding, continuity of standards between both individual years in primary schools and between primaries and secondaries, as well as on staffing.