* ECB buys more German debt after Apr redemptions

* Italian, French debt stock still well above capital key (Adds detail)

FRANKFURT, June 4 (Reuters) - The European Central Bank slowed its purchases of Italian government bonds last month, just as investors were offloading them on fears of a eurosceptic government taking power in Rome, ECB data showed on Monday.

The ECB bought 3.6 billion euros ($4.22 billion) worth of Italian government bonds and 4.2 billion euros of French debt as part of its stimulus programme in May, in each case roughly 8 percent less than its rules dictate, according to Reuters calculations on ECB data.

The ECB explained the reduced purchases by saying it needed to buy up more paper from Germany, where a large amount of debt had expired in April.

The bank was seeking to counter speculation in Italy that it had deliberately bought less of that country’s debt to influence the formation of a new government in Rome, where the president vetoed the appointment of a eurosceptic finance minister amid a market storm.

“This is the result of agreed and communicated rules on the timing of re-investments during the net purchases phase,” an ECB spokesman said.

“German bond redemptions were high in April 2018 and... had to be spread also to May 2018 to ensure a smooth implementation,” he added.

Indeed, the ECB bought 6.9 billion euros of German bonds last month, making up for record-low purchases a month earlier as it had announced.

Italy’s two main anti-establishment parties eventually managed to form a government late last week but eurosceptic economist Paolo Savona was not given the finance ministry after the presidential veto.

The ECB did not intervene in the market rout that engulfed Italy, sending its borrowing costs soaring, because indicators showed no sign of stress among banks, sources close to the matter told Reuters last week.

France and Italy, whose governments have large stocks of debt and run deficits, have benefitted from over-sized ECB purchases for years.

The ECB’s holdings of French and Italian debt is nearly 5 percent larger than the rules of the stimulus programme would indicate based on the size of their economies. ($1 = 0.8534 euros) (Reporting By Francesco Canepa; Editing by Gareth Jones)