European stock markets and the euro fell on Friday on fears that EU leaders were struggling to come to terms on immediate measures to halt the slide of euro zone government bond markets after two years of deepening crisis.

EU leaders agreed stricter budget rules for the euro zone at a summit seen as crucial to the future of the single currency in Brussels, but failed to secure changes to the EU treaty among all 27 member states, meaning a deal will instead have to involve just euro zone states and any others that want to join.

After 10 hours of talks there was little concrete progress among the leaders, apart from their commitment to work towards a new fiscal compact.

Fiscal discipline can't be achieved overnight and in the meantime, credit contraction will intensify, so the most urgent task for policymakers is to ensure decisive measures are taken to put a firm cap on bond yields and relieve funding pressures, said Takeo Okuhara, a fund manager at Daiwa SB Investments in Tokyo.

The headlines stepped up more pressure on the European Central Bank to expand its bond purchases and to have common euro zone bonds as these are the only ways to contain the debt crisis from falling into a negative spiral, he said.

Sentiment had already worsened late Thursday after ECB President Mario Draghi appeared to rule out several options that have been discussed as ways of providing a more decisive backstop to European governments and banks.

The euro was down about 0.3 percent at $1.3310 near lows seen earlier in Asia. Europe's key stock index, the FTSEurofirst 300 <.FTEU3>, opened 0.8 percent lower and most of the region's stock markets were seen following suit.

The widely watched MSCI world equity index <.MIWD00000PUS> was down around 0.65 percent.

(Additional reporting by Atul Prakash; editing by Patrick Graham)

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