The falls came after the head of the Eurogroup of eurozone finance ministers suggested that the Cyprus model, which involves a tax on bank deposits, could form a template in any future bailout.
On Monday morning, hopes the deal would solve the crisis lifted shares.
By 15:30 GMT, all major European markets had fallen into negative territory, joined by US stocks.
The president of Cyprus, Nicos Anastasiades, later addressed his country in a television broadcast.
The deal was "painful" but the best that could have been struck under the circumstances, he said.
He said that controls limiting restricting the movement of capital would be temporary and he promised to protect the weak, saying that welfare payments would be met.
Earlier, markets in Europe and the US moved downwards when Jeroen Dijsselbloem, the Dutch Finance Minister who as head of the Eurogroup played a key role in the Cyprus negotiations, said the deal represented a new template for resolving future eurozone banking problems.
"If there is a risk in a bank our first question should be 'OK, what are you in the the bank going to do about that?'," he told Reuters and the Financial Times.
He later added a clarification saying that Cyprus was "a specific case with exceptional challenges".
The Cyprus deal puts the burden for dealing with problem banks on their shareholders and creditors - in this particular case, customers with large bank balances - rather than the government and taxpayers - and bondholders, who lend through financial markets.
Our World Economics Editor, Andrew Walker, pointed out the more usual approach to failing banks in the current crisis has been for the state to inject new capital.
He says that Cyprus's banks are unusual in that they have relatively low amounts of financial market investors which could be tapped.
In the past, nations such as Ireland have pumped billions of taxpayers' money into propping up their banks, rather than risk upsetting large investors and spooking the financial system.
Mr Dijsselbloem said the pattern for bank rescues should see shareholders take the first hit, then bond holders, who lend money through financial markets, and only then should depositors with large bank balances be tapped.
By Stephanie FlandersEconomics editor
But Mr Dijsselbloem's remarks raised fears that other European countries with struggling banks may face the same solution as Cyprus, which agreed to force those with cash on deposit above 100,000 euros (Â£85,000), many of whom are Russian, to pay a substantial tax.
Cyprus will receive 10bn euros ($13bn; Â£8.5bn) in bailout funds, but has agreed to a major restructuring of its banks.
Small savers will be protected but Cyprus's second largest bank - Laiki Bank - will be wound up and split into "good" and "bad" banks, with its good assets eventually merged into the Bank of Cyprus, the country's biggest bank.
The two banks will remain closed until Thursday, while all others will reopen on Tuesday after being closed for more than a week, Cyprus's central bank says.
By Robert PestonBusiness editor
The Cypriot government suggested that account holders with deposits of more than 100,000 euros should expect to lose about 30% of their balances.
The UK's FTSE 100 index ended the day down 0.2%, while Germany's Dax gave up 0.5%, and France's Cac lost 1.1%. In New York, the Dow Jones was 0.5% lower.
In Madrid, the market slipped 2.5% while the Milan index was down 2.27%.
The euro was also driven lower, falling to a six-week low against the pound. The euro was down 0.6% to 84.74 pence.
Jeroen Dijsselbloem
The new deal for Cyprus, unlike previous agreements, does not require the approval of the Cypriot parliament.
The uncertainty over the future of Cyprus in the eurozone was sparked a week ago when its parliament rejected an earlier bailout deal, which also included a controversial bank levy.
Despite the Cypriot economy's relatively small size, many analysts had been concerned that the crisis would spread to the wider eurozone, had Cyprus been forced to give up the single currency.
There were fears that the country's possible exit from the euro would trigger a loss of confidence across the single currency bloc, and prompt investors to withdraw from other troubled economies, such as Greece.
However, while Cyprus is now likely to remain in the eurozone, the country still faces significant obstacles as it attempts to recover from the crisis.
The EU-IMF deal involves a massive restructuring of the Cypriot banking system, as well as austerity measures and tax increases.
There has also been significant public anger in Cyprus at the intervention of European authorities, and the credibility of the Cypriot government has been questioned.
"We see a risk that Cyprus' sovereign debt burden post-bailout might not be sustainable, as the country is likely to enter a deep recession caused by the shrinkage of the banking sector and severe deleveraging," warned Reinhard Cluse, an economist at UBS.
European and US stock markets have fallen despite the agreement of a bailout deal for Cyprus.