His Italian counterpart, Mario Monti, will meet Van Rompuy on Wednesday and head to tripartite talks with French President Nicolas Sarkozy and German Chancellor Angela Merkel in Strasbourg on Friday.
In Spain, the markets will be analysing the outcome of today's general elections, where the strong favourite was the conservative opposition.
Ahead of the vote, the country's 10-year bond costs came within a hair's-breadth of the 7 per cent level that is deemed unsustainable.
Greece, Ireland and Portugal all had to turn to help from the EU and International Monetary Fund (IMF) when they reached this threshold.
Opinion polls suggests the governing Socialists will be punished by voters. Unemployment in Spain is 21.5 per cent, the highest in the industrialised world, and recession looms in 2012.
The election's front-runner, Popular Party leader Mariano Rajoy, stressed spending cuts would apply to all areas except pensions.
"Spain needs to send a message that it takes the issue of the public deficit seriously," he told the daily El Pais.
He begged markets to give the next government "more than half an hour" to confront an unprecedented crisis.
Investment bank Barclays Capital said Popular Party reforms "would undoubtedly be welcomed by markets, yet may not be enough to stabilise Spanish debt.
"Ultimately, we think it likely that the ECB [European Central Bank] will need to step up its support," it said in a research note.
France, even though it carries a top-of-the-line "AAA" rating for creditworthiness, had to promise last week more than twice as much interest as Germany in raising new bonds.
The reason is that investors consider German bonds to be a safe haven, whereas France remains under a cloud over its economic management.
The rating agency Moody's warned in October of a possible downgrade in France's coveted rating, and the European Commission has said France's belt-tightening does not go far enough.
"The weeks to come will be decisive. Together we will succeed," Sarkozy said in a letter to welcome Italy's Monti.
Meanwhile, a tense debate is brewing over how the euro catastrophe was allowed to occur and what to do to prevent future crises. Strains were visible last Saturday at a summit in Berlin between Merkel and British Prime Minister David Cameron, who have fallen out over the role of the ECB.
Cameron has called on the ECB to be deployed as a "big bazooka" to end market turmoil. As a lender of last resort, the ECB would buy bonds of debt-burdened countries to keep their economies - and the euro - afloat.
But this is anathema to Germany, where the folk memory remains scarred by the hyper-inflation of the 1920s. Printing money wiped out the country's middle class and sowed the seeds for Nazism.
Cameron's stance irritates Berlin, which sees it as meddling by a euro-sceptic and a country which has refused to adopt the single currency.
PAIN IN SPAIN
* €128.1 bn- bad bank loans
* 9.3 pc of GDP - deficit
* 5 million - jobless
* 21.8 pc - people below poverty line
* 91,509 building permits in 2010 - compared with 734,000 in 2006
* 1.5m - unsold homes
