Majority Sunni Muslim Turkey has said it supports the Saudi-led operation against Iran-allied Huthi Shiite rebels in Yemen to restore order in the country.
Meanwhile Iran announced Monday it had "invited" the Turkish envoy to the foreign ministry for an explanation after Erdogan said last week that Tehran's bid for domination of the region could no longer be tolerated.
"We are keeping the programme of our visit (to Iran) but we are watching developments in Yemen," Erdogan told reporters at Istanbul airport before heading on a visit to Slovenia, Slovakia and Romania.
"The developments in Yemen are for us very, very important," he said.
In another jab at Iran after arriving in Slovenia, Erdogan said all those outside Yemen "involved in this attack against its territorial integrity" should leave now.
As a Sunni power, Turkey and the ruling Islamic-rooted Justice and Development Party (AKP), has long had complicated ties with the Shiite theocratic leadership in Tehran.
Turkey is anxiously watching the growth of Iran's influence in Iraq, its support for Shiite group Hezbollah in Lebanon and backing of the Syrian regime.
"Turkey's initial aim of a relatively healthy working relationship with Iran is increasingly unattainable," said Faysal Itani of US-based think tank Atlantic Council.
"Judging from Erdogan's statements on Iranian regional hegemony, there is no longer any way to disguise the two countries' geopolitical differences," he told AFP.
After a joint Turkish-Brazilian bid in 2010 to settle the Iranian nuclear crisis, Ankara also found itself sidelined as Washington talked directly to Tehran.
Despite their disagreements however, both countries have kept dialogue channels open and Turkey is heavily dependent on imported energy from Iran.
- 'Turkey's strategic blunders' -
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The dispute over Saudi-led strikes against the Shiite rebels in Yemen has provoked a new crisis in ties. Erdogan said in Slovenia Turkey could provide Saudi with "logistics and intelligence support for this operation at any time."
The row appears the most serious between the two sides since a 2011-2012 dispute over the installation of part of a NATO missile shield on Turkish territory, though Ankara insisted at the time it was not aimed against Turkey's neighbour.
Erdogan said on Thursday: "Iran is deploying all its efforts to dominate the region. How can that be tolerated?"
"This has begun annoying many countries in the region: us, Saudi Arabia, Gulf countries. This really cannot be tolerated."
Iran's Foreign Minister Mohammad Javad Zarif in response launched a savage attack on Erdogan, accusing Turkey of wreaking havoc in the Middle East with over-ambitious policies.
"Those who have caused irreparable damage with their strategic blunders and ambitious policies had better adopt responsible policies aimed at using the existing capacities for establishing peace and convergence in the region," he said.
Turkey's charge d'affaires was "invited" to respond to "the Islamic republic's objection and regret over Erdogan's inappropriate and unusual comments," the Iranian foreign ministry said in a statement Monday.
A Turkish official, contacted by AFP, said Ankara would not retaliate by inviting the Iranian envoy to the foreign ministry.
Erdogan stood behind his comments on Monday and rebuffed calls from senior parliament officials in Tehran who warned at the weekend that they could cancel his visit to Iran, due on April 7.
"They are not my interlocutors," said Erdogan.
"It's not those people who will determine our visit. We go or not go. It is us who will make a decision."
The row with Shiite Iran comes amid signs of warming Turkish ties with fellow Sunni Muslim kingpin and Iran's rival Saudi Arabia under new King Salman, after a chill caused by the ousting of the pro-Ankara Egyptian president Mohamed Morsi.
"Erdogan's trip to Iran is an insult to our people and a betrayal of the resistance," Hussein Shariatmadari, the editor of Iran's leading conservative newspaper, Kayhan, said on Sunday.