Merkel, who faced angry anti-austerity protests during her last visit in 2014, was to hold talks with Prime Minister Alexis Tsipras and address the still thorny issue of an impending name change for Macedonia.
The former constituent part of Yugoslavia shares the name of a northern Greek province.
Tsipras and Macedonian counterpart Zoran Zaev have agreed in principle for Skopje to switch to "the Republic of North Macedonia."
But Skopje lawmakers have still to vote through a move which entails four constitutional amendments and requires two thirds support in parliament.
The European Union backs a switch which would open the door to membership in the bloc and also in NATO.
Merkel visited Skopje before last year's referendum on the change to show support. Yet the issue remains divisive in Greece where one party in Tsipras's coalition opposes it, threatening his parliamentary majority.
The main conservative New Democracy opposition is also against the name change and wants new elections which are officially not due before October.
Merkel was to address the subject in Friday talks with President Prokopis Pavlopoulos and then with New Democracy leader Kyriakos Mitsotakis, whose party is an EU Parliament ally of her Christian Democrats.
Ahead of her visit, Merkel's spokeswoman Martina Fietz said she and far-left leader Tsipras would discuss "European and international" issues with Pavlopoulos and business representatives.
Tensions were high between Berlin and Athens during the eurozone sovereign debt crisis when Merkel's government insisted on tough austerity measures for Greece in return for international bailouts.
But, "four months from European elections, Angela Merkel's visit will underline European solidarity with Greece, a success for Europe," Thanos Veremis, professor of political history at the University of Athens, told AFP.
Greek daily Kathimerini quoted Merkel as saying Greece had its full support as she embarked on her visit saluting the "close ties" between the two EU states and NATO partners.
"I know that the past few years have been very difficult for many people in Greece. Europe showed its solidarity through three rescue programmes and supported Greece in its course of reforms towards fiscal and economic stability," Kathimerini quoted the German leader as saying, hailing the "great
progress" made since.