PRAGUE, June 3 (Reuters) - Leaders of the ruling Czech centre-right coalition agreed late on Monday to exempt children from paying for doctor visits, softening an unpopular reform aimed at cutting waste in the state health care system.

The government introduced the 30 crown ($1.86) charges for seeing a doctor and for prescriptions in January. The measures sparked protests among Czechs who, after decades of free healthcare during communist rule, consider it a basic right.

The right-wing Civic Democrats (ODS) backed down under pressure from their two junior partners who had threatened to block further reforms in the sector unless the fees, which cost about as much as a metro ticket, were scrapped.

"Children up to six years of age will be exempted from the fees," Prime Minister Mirek Topolanek said on Czech radio.

Healthcare reforms have sparked controversy across former communist central Europe, where governments are trying to overhaul public services.

In Hungary, the government lost a coalition partner due to rifts over reforms, and in Slovakia leftist Prime Minister Robert Fico struck down fees introduced by his predecessor.

The Czech cabinet has won praise from analysts and rating agencies for cutting the budget deficit, squeezing welfare and preparing pension reforms.

But, lacking a parliamentary majority and facing infighting among the ruling partners, Topolanek's cabinet has found it increasingly difficult to push through legislation.

The unions have called a one-hour general strike for June 24 to protest against the reforms, which also include a plan to turn insurers into for-profit joint stock companies.

The fees were upheld by the country's constitutional court last week, but will face a further challenge in parliament from the leftist opposition. (Reporting by Jan Lopatka; Editing by Michael Winfrey)

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