Such a flurry of visits has become commonplace recently as Erdogan's Islamist-rooted government pushes ahead with a quest for "soft power" in a region its Ottoman forebears ruled for centuries.
It has mended fences notably with Syria and Iran after decades of enmity.
The drive towards the East gathered steam amid growing frustration with European opposition to Turkey's EU bid.
But some observers in the West -- and inside Turkey itself -- were dismayed to see the leaders of a NATO country in warm embraces with the heads of Iran or Sudan.
Ankara says it remains committed to EU membership, arguing that increased regional influence will raise Turkey's strategic value in European eyes.
It rejects charges that the new vision focuses on Islamic nations, pointing to its historic bridge-building deal with Armenia and efforts at better ties with Greece and Serbia.
"Turkey is expanding its foreign policy, not shifting it," Sedat Laciner from Ankara's USAK think-tank wrote in a recent article.
"Maybe Turkey should improve its ties with 'better countries'... but the problem is that Turkey's neighbours are Syria and Iran, not Germany and France," he said.
Foreign Minister Ahmet Davutoglu, the architect of the "zero problem with neighbours" policy, detests the "Neo-Ottoman" label some use to describe Turkey's comeback in the Middle East.
Turkey, he argues, aims not at dominance but at building mutual trust and boosting economic ties to stabilise a conflict-plagued region.
"This is the EU spirit. Turkey is following the EU not the Ottoman experience," Laciner said.
Trade figures show the drive has already opened up new venues for Turkish enterpreneurs: the share of exports to Muslim nations increased from 24 percent of the total in 2006 to more than 28 percent in 2008. Sales to Egypt, for instance, doubled.
Ankara has signed a series of trade pacts and visa-free travel deals with regional countries and revamped rail links to eastern neighbours.
It has mediated in Syria's disputes with Iraq and Saudi Arabia, sought to help the West in nuclear tensions with Iran and organised four rounds of indirect talks between Syria and Israel.
Israel's devastating war on the Gaza Strip at the turn of the year not only shattered the talks, but marked a sharp downturn in relations with Ankara, a long-time ally.
Turkey excluded Israel from joint military drills in October, dealing a fresh blow to ties already bruised by its hosting of Hamas leaders in 2006.
Erdogan stirred more controversy when he played down concerns Iran may be developing an atomic bomb and fingered Israel, widely considered the region's sole if undeclared nuclear power.
And in November, he defended Sudanese President Omar al-Beshir, indicted for war crimes in Darfur, saying "no Muslim could perpetrate a genocide."
Erdogan's rhetoric fed criticism that religious allegiances guide the policies of his Justice and Development Party (AKP), the moderate offshoot of a now-banned Islamist movement.
"The drift away from the West is the most important paradigm change in Turkish foreign policy since the Cold War," Soner Cagaptay from the Washington Institute for Near East Policy said in a recent article.
"Were the AKP's foreign policy simply to reflect empathy for Muslims, that would be quite normal. But instead, the move seems to be toward alignment with regimes holding expressly Islamist and anti-Western worldviews," he said.
Others agree Erdogan's outbursts were damaging, blaming the premier for catering to Islamic grassroots, but insist Ankara's expanding vision is on the right track.
"The policy is essentially successful... Unfortunately Erdogan has provided ground for those who are irked by Turkey's growing regional influence to criticise the AKP," international relations expert Mensur Akgun said.
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