Finance Minister Wolfgang Schäuble invited his counterparts from Britain, Canada, France, Italy, Japan and the United States to the eastern city for an "in-depth exchange of views" on a number of questions.
Issues on the official agenda range from the state of the global economy, to financial regulation, fighting tax evasion and ways of starving terror groups like the Islamic State of funding.
But it was the Greek crisis that was at the forefront of everyone's minds, after Athens prematurely declared a day earlier that a deal was imminent but was then forced to back-pedal as its creditors were more sceptical.
Berlin insists that the G7 -- of which Greece is not a member -- is not the correct forum for the debt talks, anyway.
But with all of the other key actors present -- notably International Monetary Fund chief Christine Lagarde, Eurogroup president Jeroen Dijsselbloem, European Central Bank chief Mario Draghi and EU monetary affairs commissioner Pierre Moscovici -- the subject loomed large.
On Wednesday, Athens had said it was close to a deal that would unlock badly-needed bailout funds for its struggling economy.
'Not there yet'
But the European Union poured cold water on that optimism on Thursday.
"We're not there yet. There are open issues which need to be resolved," European Commission spokeswoman Annika Breidthardt told reporters in Brussels when asked about the negotiations.
EU monetary affairs commissioner Moscovici said the same in Dresden.
"It is wrong to say, like the Greeks have, that we've gone three-quarters of the way to reaching a deal," he told French public radio, France Culture, on the sidelines of the meeting.
"We are beginning to see reform projects that are consistent," Moscovici continued, but added: "There's still a lot of work to do."
G7 host Schaeuble also denied there had been any new significant breakthroughs.
Discussions "have not really progressed much further," he told ARD German public television on Wednesday evening, adding that he was "also a bit surprised that Athens is always saying that a deal is imminent."
But it is not just the Europeans who insist that Greece's fate in the eurozone is a matter of urgency.
IMF chief Lagarde, interviewed by German television, said there was "still a lot of work to do" and no "substantial result" had yet been achieved.
"Everyone has to double down, and treat the next deadline as if it's the last deadline and get this resolved," said US Treasury Secretary Jack Lew.
The ECB warned that the Greek crisis could pose a risk to financial stability in the euro area in the future.
A Greek government spokesman said Thursday they hoped for a deal by Sunday.
"A deal is possible," Moscovici insisted, adding that if talks had foundered, "I would tell you."
Meeting of experts
For the first time at a G7 finance meeting, a number of the world's leading economists -- such as Nouriel Roubini, Kenneth Rogoff and former US treasury secretary Larry Summers -- are among those invited.
The G7 ministers will also examine the current high level of volatility on the financial markets.
The Chinese currency, the yuan or renminbi, could also feature in discussions, as Beijing continues to push for it to play a greater role in the world financial system, such as being included in the basket that makes up the IMF's own "special drawing rights" reserve currency.
Washington has long claimed that the yuan was manipulated, but the IMF said on Tuesday that the currency is "no longer undervalued".
The meeting began late Wednesday with a short ceremony in Dresden's rebuilt Frauenkirche church, which was almost totally destroyed in bombing by the British and US allies during World War II and the remaining ruins were left as a war memorial for more than 50 years.
But it was painstakingly rebuilt following German unification and reconsecrated in 2005.
The finance ministers' meeting, which is in preparation for a wider summit of G7 leaders in southern Germany starting June 7, was scheduled to wrap up on Friday.