It reaffirmed France's top-notch triple-A rating but even here said the outlook was now negative over a longer term.
Underscoring the tensions within the bloc over the crisis that has spread relentlessly over the past two years, Italy's prime minister earlier urged European policymakers to beware of dividing the continent with their efforts to fight its debt crisis, warning against a "short-term hunger for rigor" in some countries, in a swipe at Germany.
Germany has led resistance to allowing the European Central Bank to ramp up its buying of government bonds on the open market to a big enough scale to douse the crisis.
Fitch said that following the EU summit a week ago it had concluded that "a 'comprehensive solution' to the eurozone crisis is technically and politically beyond reach.
"Of particular concern is the absence of a credible financial backstop. In Fitch's opinion, this requires more active and explicit commitment from the ECB to mitigate the risk of self-fulfilling liquidity crises for potentially illiquid but solvent Euro Area Member States," Fitch said.
It put Belgium, Spain, Slovenia, Italy, Ireland, and Cyprus on negative watch. Another ratings agency, Standard & Poor's, had already warned 15 of the currency bloc's 17 members they were close to a downgrade.
Earlier German Chancellor Angela Merkel gained somee respite from domestic pressure to take a tougher line in the euro zone crisis when Eurosceptics hostile to more bailouts lost a referendum in her junior coalition partner, the Free Democrats, aimed at blocking a permanent rescue fund.
Meanwhile, a first draft of a planned fiscal union treaty among euro zone countries and aspiring members, published on Friday, showed that countries could be taken to the European Court of Justice if they fail to meet agreed budget targets.
Merkel - under pressure from the revered Bundesbank to force debt-saddled euro zone countries to reform and save their way out of crisis with austerity measures - has led a push for automatic sanctions for deficit "sinners" in the bloc.
This has fed concerns that excessive belt-tightening in southern countries could send their economies into a negative spiral with no prospect of growing out of the crisis, while feeding resentment in the prosperous north.
Italian Prime Minister Mario Monti said Europe's response to the debt crisis "should be wrapped in a long-term sustainable approach, not just to feed short-term hunger for rigour in some countries.
"To help European construction evolve in a way that unites, not divides, we cannot afford that the crisis in the euro zone brings us ... the risk of conflicts between the virtuous North and an allegedly vicious South," he told a conference in Rome.
In Germany, turnout in the FDP bailout referendum fell short of the necessary quorum of one-third of the party's membership, and only 44.2 percent voted for dissident lawmaker Frank Schaeffler's motion against the planned European Stability Mechanism.
A victory for the Eurosceptics could have brought down Merkel's centre-right coalition, but the outcome still left the FDP split, with its public support in tatters.
French officials have sought to prepare the public for the likelihood that Paris will lose its top-notch rating from S&P for the first time since 1975, playing down the potential setback and focusing attention instead on neighbouring Britain.
"The economic situation in Britain today is very worrying, and you'd rather be French than British in economic terms," Finance Minister Francois Baroin said in a radio interview, a day after Bank of France governor Christian Noyer said that if ratings agencies were even-handed, Britain deserved to be downgraded before France.
Britain's Deputy Prime Minister Nick Clegg said French Prime Minister Francois Fillon had called him to explain that "it had not been his intention to call into question the UK's rating but to highlight that ratings agencies appeared more focused on economic governance than deficit levels."
Clegg's office said he accepted the explanation "but made the point that recent remarks from members of the French Government about the UK economy were simply unacceptable and that steps should be taken to calm the rhetoric."
Euro zone officials said potential downgrades, particularly from S&P, could raise the cost of borrowing for the region's existing EFSF bailout fund but would not make a big difference to its operations.
EFSF chief Klaus Regling told the Rome conference there was about 600 billion euros available to fight the crisis, more than Italy and Spain's combined funding needs for 2012.
"If Italy and Spain were to ask for support their gross financing needs for 2012 are less than that and I don't think they would need to be taken off the market," he said.
The EFSF has the option of providing first loss insurance on new bond issues, but the country concerned would have to make a formal request and negotiate conditionality, while the sum guaranteed would have to be agreed unanimously by EFSF members, subject to German parliamentary approval.
Euro zone countries are to hold a conference call next Monday to agree on a boost to the International Monetary Fund's lending capacity, as part of measures to help cope with the debt crisis, to which they will commit 150 billion euros, Slovak Finance Minister Ivan Miklos told Reuters.
The United States has refused to offer any additional funding and it remains to be seen how much non-European economies such as China, Russia, Brazil and India are willing to commit.
The European Central Bank has resisted calls to embark on unlimited purchases of euro zone sovereign bonds to quell the debt crisis, putting the onus back on governments and their collective financial firewalls.
ECB President Mario Draghi said on Thursday that euro zone governments were on the right track to restore market confidence and the ECB's bond-buy plan was "neither eternal nor infinite".
But in one intriguing hint on Friday, Bank of Italy governor Ignazio Visco told the Rome conference: "The impression is that there is only one way to convince markets and we'll work on that." He did not elaborate.
The comments came amid growing signs that banks are resisting pressure from governments to come to the aid of debt-choked euro zone countries by using cheap money lent by the ECB to buy more sovereign bonds.
With euro zone governments needing to sell almost 80 billion euros of fresh debt in January alone, the stand-off between policymakers and banks could turn the slow-burning debt crisis into a conflagration in the New Year.
The chief executive of UniCredit, one of Italy's two biggest banks, said this week using ECB money to buy government debt "wouldn't be logical".
In Greece, where the debt crisis began two years ago, a senior official of the EU/IMF troika team negotiating terms for a second bailout package said there was no guarantee that talks on the private sector's contribution would lead to a voluntary deal involving the bulk of its creditors.
Agreement has been held up by wrangling over issues ranging from the credit status and interest coupons on the new bonds to legal guarantees to be offered by the official sector.
