The comments came in a joint statement following a telephone conversation on Sunday.
They echo remarks from French President Francois Hollande and European Central Bank (ECB) President Mario Draghi.
It has increased speculation that the ECB could resume its programme of buying up Spanish bonds.
The remarks came the day before a visit from US Treasury Secretary Timothy Geithner.
On Monday, he will be meeting German Finance Minister Wolfgang Schaeuble before flying to Frankfurt to meet Mario Draghi.
Markets rallied on Thursday following Mr Draghi's supportive comments.
The BBC's Stephen Evans in Berlin said that Mr Geithner's whirlwind visit combined with the remarks from eurozone leaders had raised speculation still further that a quiet change of policy was underway.
Eurozone leaders agreed in a summit at the end of June that they would allow their rescue fund to intervene on bond markets.
But since then there has been growing doubt as to whether the ECB could buy bonds from troubled economies if the eurozone's richest country, Germany, opposed the policy.
There may be further signs of the support that some eurozone economies need on Monday, when Italy auctions three, five and 10-year bonds.
Monday will also see the release of the first estimate of whether Spain's economy grew or contracted in the three months from April to June.
It is expected to show that Spain's recession continued.
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