London(CNN) Two days after UK voters decided they wanted to leave the European Union, foreign ministers from the EU's six founding countries met in Berlin to discuss the speed and strategy of Britain's exit.
European Commission President Jean-Claude Juncker has said he'd like to get started on it "immediately."
"Britons decided that they want to leave the European Union, so it doesn't make any sense to wait until October to try to negotiate the terms of their departure," Juncker said Friday, referring to British Prime Minister David Cameron's announcement that he would step down -- but not before a new leader could be installed in October.
However, German Chancellor Angela Merkel suggested there's no hurry.
"What's important is that Great Britain has not put into motion this proposal, and also the agreement isn't finished," she said Saturday.
"Great Britain continues to be a full member of the EU with all rights and responsibilities. I also spoke to the British Prime Minister about that and he confirms the same.
"We were sad yesterday that the vote went that way. And that is no reason to be in a way especially nasty during the negotiations, but that must be properly dealt with," Merkel added.
In an interview with German broadcaster ARD, Juncker said he, too, was deeply saddened by the UK's 52%-48% vote.
"It is not an amicable divorce, but it also wasn't a tight love affair," he said of the EU's relationship with Britain.
In a statement following the meeting in Berlin on Saturday, the foreign ministers of Belgium, France, Germany, Italy, Luxembourg and the Netherlands said they "expect the UK government to provide clarity and give effect to this decision as soon as possible."
"We stand ready to work with the institutions once the negotiations in order to define and clarify the future relations between the EU and the UK will start," the statement said.
The ministers did note, however, that the UK vote was a wake-up call that potential reform is needed within the EU framework.
"We take this very seriously and are determined to make the EU work better for all our citizens," they said. "We have to focus our common efforts on those challenges which can only be addressed by common European answers, while leaving other tasks to national or regional levels."
Many "Leave" voters in the UK were unhappy with decisions being made for them in Brussels by unelected EU officials.
European Parliament President Martin Schulz called Cameron's decision to wait until October to step down "scandalous," saying that by waiting, Cameron -- who championed the "Remain" campaign -- was "taking the whole (European) continent hostage."
Britain's European Commissioner Jonathan Hill announced Saturday that he will resign following the UK's decision to leave.
In a statement, he said he was "very disappointed," but "what is done cannot be undone."
Johann N. Schneider-Ammann, president of the Swiss Confederation, said that the Swiss-UK relationship needs to be reconfigured in light of the referendum results and noted that a working group formed a few weeks ago in case of a "Leave" win has stepped up its activity. Switzerland is not a member of the EU.
"The British decision raises many questions -- for the United Kingdom, for the EU and for Europe as a whole. And also for Switzerland. Switzerland will continue to take all the necessary steps to safeguard our country's interests," he said in a speech Friday.
Switzerland "will continue to have a major interest in close relations with the United Kingdom, an important partner, not least in the economic area," Schneider-Ammann said. But economic ties and "the free trade agreement in particular -- will have to be redefined."
"It is to be expected that today's decision in the United Kingdom will exacerbate the insecurity about Europe's economic development. This will also have a negative impact on Switzerland as a business location and will make it more difficult to find a solution with the EU on the migration question. "
Slovenian Prime Minister Miro Cerar said he respects "the democratically expressed will of the British people," but also regrets the results of the vote. His remarks were in a news release issued Friday.
Cerar said he thinks that after a "brief period of relative uncertainty on the international markets," the development will "result in additional strengthening of the Union and incentives to carry out its reform that will allow us to face similar challenges more effectively, with a greater measure of solidarity and determination, and in a closer partnership."
He said Slovenia is "strongly committed to further enhancement of the European Union. "
"As its Member State, it does not expect that United Kingdom exiting the European Union will bring any major direct consequences for Slovenia. The long-term consequences of United Kingdom's decision, however, will depend on the newly agreed form of cooperation between the UK and EU," he said.
He said he expects Cameron will notify Slovenia and other nations about the UK decision to depart from the EU and that the exiting procedures will be started soon, "pursuant to the Treaty of Lisbon."
Meanwhile, more than 2 million people have signed a petition on the UK Parliament's website demanding a second referendum on whether to leave the EU.
At one point, the website crashed after being unable to deal with the surge of traffic.
By law, all petitions to the site that receive more than 100,000 signatures must be considered for debate in Parliament.
The petition calls for a new rule to be implemented that would require another referendum on the EU question if the remain or leave vote is less than 60% based a turnout of less than 75%.
Amid the confusion and uncertainty, credit agency Moody's announced it had downgraded the United Kingdom's credit outlook to "negative." It said the referendum result will lead to "a prolonged period of uncertainty for the UK, with negative implications for the country's medium-term growth outlook."
And this is just the beginning.
"During the several years in which the UK will have to renegotiate its trade relations with the EU, Moody's expects heightened uncertainty, diminished confidence," it said in a statement.
Read: Why are the Brits thumbing their noses at Europe?
Ahead of Saturday's EU meeting, German Foreign Minister Frank-Walter Steinmeier struck a more cautious tone, stating it is crucial to preserve the "project of freedom and stability."
"It is completely clear that we now have a situation that allows for neither hysteria nor paralysis," Steinmeier told reporters.
"We must not resort to hectic activity, and act as if all the answers are ready. But after the British decision, we mustn't lapse into depression and inactivity."
He added: "I am confident that these countries can also send a message that we won't let anyone take Europe from us."
Read: Rocky marriage ends in sudden divorce
In Paris, United Nations Secretary-General Ban Ki-moon welcomed the talks between the EU and the UK after meeting with French President François Hollande.
"I trust the fact that these talks will take place in a positive and pragmatic way," he said.
"On the other hand, the U.N. will continue our collaboration with the UK and the EU -- both important partners."
Ban said he is counting on both sides to maintain their partnerships with the U.N. on development and humanitarian issues.
"It's clear that when we work together, we are stronger," he said.
Meanwhile, Scottish First Minister Nicola Sturgeon met with her Cabinet on Saturday to discuss the country's next move.
She said the Scottish government was seeking immediate discussions with the EU institutions and with other EU member states "to protect Scotland's place in the European Union." She also repeated an assertion she first made Friday that a second referendum on Scottish independence is very much an option on the table.
Scottish voters rejected independence from the United Kingdom in a 2014 referendum.
In Germany, the finance ministry drew up documents detailing how it plans to negotiate Britain's exit from the European Union, according to a report in Handelsblatt newspaper.