BUDAPEST (Reuters) - The European Union's task of boosting competitiveness to catch up with rivals the United States and China has gained fresh urgency after Donald Trump's election win, Mario Draghi said on Friday, as doubts increase that the bloc is up to the task.

Trump warned shortly before his U.S. presidential victory that the 27-nation bloc will have to "pay a big price" for not buying enough American exports and has threatened 10% tariffs on all U.S. imports.

Former European Central Bank chief Draghi, speaking at an EU summit ahead of presenting his report on EU competitiveness to EU leaders on Friday, said the sense of crisis had deepened.

"Yes, that's right. The sense of urgency today is greater than it was a week ago," he told reporters on Friday.

He was speaking about the U.S. election outcome, but could have said the same about the European Union itself after the collapse of the German government on Wednesday. Given French President Emmanuel Macron's domestic problems, the Franco-German engine normally driving the EU is weakened if not broken.

Luxembourg's Prime Minister Luc Frieden said that in all its neighbouring countries - Belgium, France and Germany - there was no government with a parliamentary majority. The EU, he said, needed strength not instability to solve major challenges.

EU leaders are expected to sign off on the "Budapest Declaration" on Friday, a long to-do list with multiple deadlines for a deeper single market, more capital for investments and a unified energy market.

Draghi has said the bloc needs additional investment of 750-800 billion euros per year, but frugal EU countries have already taken issue with the idea that some of this should come from joint EU assets.

On Friday, Draghi said the most urgent thing to do was not joint funding, but to tackle fragmentation of the single market and of capital markets.

But discussions on a Capital Markets Union (CMU) have dragged on for a decade because of entrenched national interests, different business cultures and regulations in EU members.

It is just the sort of issue a Franco-German consensus could drive to the finish line, but the two are at odds over a French idea to allow a small group of countries to press ahead.

Belgian Prime Minister Alexander De Croo said the EU needed to pull together ahead of Trump's return to the White House, explain to him the impact of a tariff war and be clear that they should discuss the economic behaviour of their common competitor China.

Eurointelligence wrote on Friday that when Trump becomes president in January, the EU would have lame duck governments in Berlin and Paris and that, rather than uniting, the bloc's members appeared instead set to compete for his attention.