Image caption The German finance minister met Mr Geithner for informal talks

A meeting between US Treasury Secretary Tim Geithner and the German finance minister has boosted hopes of imminent action on the eurozone crisis.

The pair expressed confidence in the eurozone's reform efforts and emphasised the need for coordination.

Mr Geithner met Wolfgang Schaeuble ahead of a meeting with European Central Bank head Mario Draghi.

Markets rose across Europe on anticipation of measures to tackle Spain and Italy's high borrowing costs.

Mr Geithner also discussed the crisis with French Finance Minister Pierre Moscovici by phone, the AFP news agency reported.

Spain's Ibex closed 2.8% higher, the FTSE 100 rose 1.2% and Germany's Dax jumped 1.3%.

Mr Schaeuble interrupted his holiday for the informal meeting which was held on the German North Sea island of Sylt - a luxurious resort for wealthy Germans.

They "emphasised the need for ongoing international co-operation and coordination to achieve sustainable public finances, reduce global macroeconomic imbalances, and restore growth," a joint statement said.

The two men also "expressed confidence in euro area member states' efforts to reform and move towards greater integration".

Analysis It is a measure of concern about the crisis in the European economies that US Treasury Secretary Timothy Geithner took the trouble to fly to a remote German holiday island in the North Sea to talk to his German counterpart. After meeting Wolfgang Schaeuble, the two issued a statement stressing the need for "ongoing international cooperation and coordination". What they did not say was what form that co-ordinated cooperation would take. The financial markets, though, think they have some idea. Last week, the ECB's President, Mario Draghi, said he would do whatever it took to preserve the Eurozone, the very words then echoed by the leaders of Germany, France and Italy. That was read by the markets as an intention by the ECB to buy the bonds of Spain and Italy - and Italian and Spanish government debt has got cheaper in response. All eyes now turn to the bank's monthly meeting on Thursday when Mr Draghi may or may not announce what the markets expect - so confirming the current market optimism or dashing it. Will the ECB's bond plan work?

The timing of these meetings, just three day's ahead of Thursday when the ECB will announce its latest decision on interest rates, has added to speculation that it may also announce that it is restarting its bond-buying programme, known as the Securities Markets Programme (SMP).

The SMP, which was suspended at the end of January, enables the ECB to buy government debt from banks helping to reduce the cost of borrowing for governments.

In recent days, European leaders have pledged to act in support of the eurozone.

Eurogroup leader Jean-Claude Juncker joined in late on Sunday when he called for action to cut Spain's debt costs.

"We will work in close agreement with the ECB, and we will, as ECB President Mario Draghi said, see results.

"I don't want to drive expectations, but I must say, we have reached a decisive phase," Mr Juncker said in interviews with German and French press.

Cheaper borrowing

Mr Juncker also referred to agreements at the last European Union summit regarding the European bailout fund, the EFSF.

Under the EFSF's constitution, the fund is permitted to buy government bonds on the primary market, effectively lending directly to indebted governments such as Spain.

This is important because the European Central Bank's constitution prevents it from lending money directly to governments.

It is now hoped that co-ordinated action between the ECB and the EFSF would be more effective in bringing down the borrowing costs of countries such as Spain and Italy.

Spain slowdown

Meanwhile, Italy paid a lower rate of interest at a bond auction to raise 5.48bn euros (£4.2bn).

Italy's bond auction saw it offload its 10-year bonds at an interest rate of 5.96%, the first time it has sold them below 6% since April.

However, Richard McGuire, a rate strategist at Rabobank, said the interest rate Italy was paying to sell its debt was still too high.

"While these sales do provide some indication of an easing of tensions at the periphery, they also show considerable further progress on this front is needed," Mr McGuire added.

And Spain's 10-year borrowing costs dropped again on Monday to 6.6% from last week's record high of 7.5%, reflecting a slight improvement in investor confidence.

However, Commerzbank rate strategist Rainer Guntermann cautioned that the market rally may not continue.

"Expectations are high... but for the rally to continue we may need more colour, more details and maybe some action," said Mr Guntermann.

The fall in bond yields, came despite official data which showed that Spain's economy shrank 0.4% in the second quarter of the year.

That compares with a 0.3% contraction in gross domestic product (GDP) in the first three months of the year.

The national statistics institute INE , which published the figures, said the worsening GDP figures reflected "weaker domestic demand".