The decision could cause a public backlash in Germany. Despite its position as the world's third largest arms exporter, it has had a long-held policy not to supply lethal weapons into conflict zones. Public opinion is strongly against any intervention in geopolitical crises.
The move came as France called for an international conference to discuss ways of combating Isis.
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"We have to come up with a global strategy to fight this group, which is structured, has significant financing, very sophisticated weapons and threatens countries like Iraq, Syria and Lebanon," President François Hollande said in an interview with Le Monde newspaper.
Confirming that France was supplying "sophisticated weapons" to Kurdish forces fighting the jihadis in northern Iraq, Mr Hollande said he would shortly propose a conference on security in Iraq and what he called "the struggle" against Isis.
Laurent Fabius, foreign minister, said France wanted "all countries of the region, including Iran" and the five permanent members of the UN Security Council to join in the action against Isis
Italy's parliament approved plans to arm the Kurdish forces fighting Isis. On a one-day visit to Iraq, Matteo Renzi, the prime minister, said the government was ready to consider requests for supplies of personal weapons and ammunition for self-defence.
Defence Minister Roberta Pinotti said Italy had earmarked light automatic weapons and ammunition used by the Italian armed forces, as well as arms made in the former Soviet Union and seized at sea during the 1990s Balkan wars, to be sent to Iraq.
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Mr Hollande confirmed that France was supplying weapons to so-called moderate rebels in Syria who have been eclipsed by Isis over the past year, although he said only that these supplies "conform to European commitments".
Paris backed a tough approach last year by the west in support of mainstream rebels fighting the rule of Syrian president Bashar al-Assad, including military strikes against the regime after its apparent use of chemical weapons. It was dismayed when both the UK and the US backed off from taking military action.
"The international community carries a very grave responsibility for what has happened in Syria," Mr Hollande said.
He said that had the west taken stronger action to force a transitional government in Syria "we would not have had the Islamic State [Isis]".
He added: "If, a year ago, we had had a sufficient reaction by the great powers to the use of chemical weapons, we would not have been faced by this terrible choice between a dictator and a terrorist group."