"Now is not the time to look inwards and look at institutional questions," Swedish Prime Minister Fredrik Reinfeldt told reporters at a press conference in Stockholm.
"Now is the time to show leadership," in particular ahead of a global summit on reducing greenhouse gases in December in Copenhagen, and for that "we need clarity," he said.
That clarity is clearly lacking in European institutions.
The most urgent problem facing Sweden's presidency is that it risks finding itself with a lame duck president of the European Commission.
European leaders in mid-June gave Jose Manuel Barroso their lukewarm support for his re-election for a second five-year term, and the European parliament, which must also vote on the matter, has indicated it could postpone its decision until the autumn.
That would prolong the uncertainty and could give Barroso's critics on the left, the Greens and even the liberals, time to come up with a rival candidate.
Aware of this risk, Barroso urged EU parliamentarians to find a rapid solution.
The European parliament is expected to announce on July 9 whether or not it will postpone its vote.
"We should have clarity as soon as possible ... I hope the decisions will be taken in a way that will reinforce and not weaken the European institutions," Barroso said.
Reinfeldt also called for a rapid resolution to the issue, saying parliament should present an alternative candidate if it is not satisfied with Barroso.
Sweden will also have to steer the EU through the problems posed by the Lisbon Treaty, which is aimed at streamlining decision-making in the European Union and making the bloc more influential in the world.
The future of the treaty, which has to be ratified by all 27 EU members, is in limbo pending a new referendum that Ireland will hold in early October after Irish voters rejected it in a first plebiscite in June 2008.
Opinion polls suggest the "yes" side will win the referendum, but if those predictions are wrong Europe would be plunged into a new crisis.
Apart from Ireland, three other countries have yet to ratify the treaty.
They are Germany, where the country's top court on Tuesday delayed the ratification of the document until a law protecting national parliamentary powers is passed, as well as Poland and the Czech Republic, whose presidents are dragging their feet on the issue.
If the treaty is ultimately ratified, Stockholm will then have to oversee the nominations -- and wrangling between member states -- for the new positions created in the treaty: a de facto EU president and foreign minister who will enjoy wider powers.
Despite the myriad institutional issues, Stockholm insisted Wednesday that it would be able to focus on its two main priorities -- tackling soaring unemployment in Europe and improving the regulation of financial markets following the economic crisis, and reaching a climate deal with the United States and developing countries.
Reinfeldt stressed there was "not a minute to lose" in talks to reach a deal in Copenhagen.