Eurozone debt summit July 21 in Brussels: EU president

"Our agenda will be the financial stability of the euro area as a whole and the future financing of the Greek programme," Van Rompuy said in a message on Twitter.

"I have asked the preparatory work to be brought forward inter alia by the finance ministries," he added.

EU officials have been trying to fix a summit for several days.

The fact that a date has been chosen suggests they may finally have made some headway on a second bailout for Greece, which is proving highly controversial.

But a source close to the talks said Friday that there had been progress, even if there was still work to be done.

"The difficulty isn't to find the sums...," however much it might end up being, Belgian Finance Minister Didier Reynders told AFP, rather the unresolved question revolved around the degree of private sector participation.

Germany, the eurozone's economic powerhouse, wants private sector creditors to share some of the burden of a new Greek bailout.

But the European Central Bank is adamantly opposed, fearing it would trigger a potentially disastrous default.

For Belgium, Reynders said he thought the banks should contribute 30 billion euros to Greece's second aid package -- but that contribution had to be voluntary, he warned, or it would be perceived as a default in all but name.

When Fitch ratings agency downgraded Greece by three points to CCC status on Wednesday, it gave as one of its reasons uncertainty over the role private investors would play in any second bailout.

"As previously stated by Fitch, private sector involvement would likely be viewed as a sign of sovereign credit impairment and could trigger a rating default event," said the statement from Fitch.

The EU and International Monetary Fund bailed out Greece in May 2010 with a package worth 110 billion euros ($160 billion) in exchange for a series of drastic austerity measures to stabilise its public finances.

The package has had some success but Greece is still in serious difficulty and needs another bailout estimated to be around the same amount.

The problems in Greece, however, have spread: Ireland and Portugal have also had to be bailed out, while Italy and Spain are seen to be at risk given the strained state of their public finances.

And as the debt noose tightens in Europe, markets are anxiously watching a stand-off in Washington where President Barack Obama and his Republican opponents are at loggerheads over raising the US debt ceiling.

Obama has warned that time in running out and top ratings agencies Moody's and Standard and Poor's have said they could downgrade their top-notch US rating if Washington does not reach an accord by August 2 and so avoid a default.

Officials are trying to square the circle between the German position on Greece, where there is concern at making the taxpayer bail out Athens again, and the ECB's focus on defending the credibility of the euro currency.

One diplomat said efforts were under way to reconcile the conflicting agendas after weeks of uncertainty, which have seen the financial markets in turmoil on speculation that Athens cannot avoid a default.