The euro slid Tuesday and European stock markets struggled on concerns over Greece's ability to meet looming repayment deadlines, dealers said.
The dollar was also boosted by expectations the US Federal Reserve will raise interest rates in the coming months. The shared eurozone unit slid to $1.0860, down from $1.0980 late Monday.
"The euro continued to fall Tuesday with many blaming Yanis Varoufakis after the Greek finance minister pointed the finger at the country’s creditors on Monday, claiming that their wish to impose further austerity on Greece as the cause of the stalemate," said Spreadex analyst Connor Campbell.
In early afternoon deals, London's FTSE 100 index shed 0.11 percent to 7,024.10 points and Frankfurt's DAX 30 dipped 0.47 percent to 11,759 compared with Friday's closing levels. Both markets were shut Monday.
In Paris, the CAC 40 added 0.38 percent to 5,136.50 compared with the close on Monday, when it had lost 0.50 percent in value.
Greece's creditors must "get their act together" and help produce a new loan deal for the cash-strapped country, Finance Minister Yanis Varoufakis said.
"It's about time the institutions, in particular the IMF, get their act together, and come to an agreement with us," the outspoken Varoufakis told CNN.
Greece's radical left government in recent days has sent conflicting messages on its finances as the state is gradually running out of money.
Greece is facing a cash crunch because Athens has been unable to agree with its creditors -- the International Monetary Fund, the European Union and the European Central Bank -- on reforms that would unlock some 7.2 billion euros ($7.9 billion) in promised bailout cash.
Over the weekend, a cabinet minister said Greece had "no money" to make a series of repayments to the IMF from June 5, but a government spokesman insisted the country would keep up payments as long as it could.
"The eurozone is on edge as the countdown begins to Greece’s next two debt repayment instalments," said Currencies Direct analyst Phil McHugh.
"Greece’s crunch point is its debt repayments to the International Monetary Fund on 5 and 12 June.
"Reports over the weekend suggest that Greece won’t be able to make these payments without striking a deal with its creditors."
Major Asian markets mostly rose Tuesday, with Hong Kong and Shanghai leading the way, while Tokyo marked an eighth straight gain to a 15-year high.
Hong Kong added 0.92 percent to 28,249.86 -- its highest close since December 2007 -- and Shanghai jumped 2.02 percent to 4,910.90 -- the highest since January 2008.
The indices were boosted by hopes for fresh Chinese measures to boost the economy as well as Beijing's decision Friday to relax rules on access to mainland financial markets.
Tokyo ended up 0.12 percent, helped by a weaker yen, hopes for corporate earnings and the Bank of Japan's ultra-loose monetary policy.
With Wall Street and most European markets closed Monday for public holidays there were few catalysts outside Asia to drive business.
The dollar has meanwhile been underpinned by growing hopes the Federal Reserve will raise interest rates in the coming months -- a view supported by comments from Fed chief Janet Yellen who said Friday she expects a hike "at some point this year".