* Focus on energy deals, but political rapprochement in air
* Turkey capitalises on opening from moderate Iran president
* Tensions over support for opposing sides in Syrian war
* But common interest in countering al Qaeda in Syria
By Parisa Hafezi
ANKARA, Jan 29 (Reuters) - Turkish Prime Minister Tayyip Erdogan has arrived in Iran to bolster trade and energy relations, state TV said, in what also looked like a bid to defuse tensions over Syria by capitalising on Tehran's diplomatic opening to regional rivals and the West.
Iran has been a strong strategic ally of Syrian President Bashar al-Assad since the start of the uprising against him, while Turkey has been one of his fiercest critics, supporting his opponents and giving refuge to rebel fighters.
But Iran's election last June of President Hassan Rouhani, a relative moderate who says he wants to thaw its ties with the West, and shared concern over the rise of al Qaeda in Syria, have spurred hopes of a Turkish-Iranian rapprochement.
While deep divisions remain between Ankara and Tehran over the conflict in Syria, diplomats and government officials say both sides want to mend a relationship that could be pivotal to the fast-changing political map of the Middle East.
The United States believes detente between Turkey and Iran is important to wider stability in the Middle East, a strategic breakthrough Washington hopes to achieve from talks that world powers are pursuing with Tehran to curb its nuclear programme.
Erdogan was to meet Iranian Supreme Leader Ayatollah Ali Khamenei as well as Rouhani, whose foreign policy of "prudence and moderation" has eased Tehran's international isolation and revived contact with longtime arch-enemy Washington.
"Our relations with Turkey have entered a new phase and we hope this trend continues. Besides serving the interests of the two countries, we hope our dialogue (with Turkey) serve regional interests as well," Iranian Foreign Ministry spokeswoman Marzieh Afkham told reporters in Tehran.
"As two neighbours and Muslim countries, Iran and Turkey enjoy many commonalities and many cooperation opportunities."
Analysts said the main focus of Erdogan's visit would be expanding economic cooperation, finessing the political disputes for now. "Considering that the economy and energy ministers are accompanying Erdogan, we can say this trip is business-targeted," said Tehran-based analyst Hossein Foroughi.
Three trade deals were signed on Wednesday after Erdogan's arrival, Iranian state television said, without elaborating.
"Today we had a good chance to review bilateral ties," Erdogan said in remarks translated into Farsi and made during a meeting with Iranian Vice President Eshaq Jahangiri shown by Iranian television.
"I would like to mention specifically, and to express my satisfaction with, the agreement we signed in the preferential trade field," he said. "It is obvious that we import from Iran crude oil and gas, which are strategic energy sources, and we (will be) able to increase the volume of these imports."
Turkey is keen to increase oil and gas imports from Tehran in anticipation of sanctions against Iran's huge energy sector being dismantled in the wake of the Nov. 24 deal between Tehran and six big powers under which the Islamic Republic committed to scaling back some of its controversial nuclear activities.
Some sanctions that were imposed over suspicions that Iran is covertly trying to develop a nuclear weapons capability, something it denies, were relaxed starting on Jan. 20.
But most sanctions, including a severe squeeze on Iran's access to the international financial system, remain in force pending a long-term agreement on the scope of Iran's nuclear programme, which is to be negotiated over the next six months.
POTENTIAL MARKET BONANZA IN IRAN
Still, the post-sanctions potential of a market of 76 million people in Iran with some of the world's biggest oil and gas reserves is a magnet for foreign investors, including Turkish companies.
"We hope the process will be finalised with an agreement that will ensure the removal of all sanctions on Iran. Turkey has so far done its best in that regard and will continue to do so," Erdogan told reporters in Ankara ahead of his departure.
Iranian officials say trade between the countries stood at $22 billion (16.2 billion euros) in 2012, before dipping to $20 billion in 2013. It is expected to reach $30 billion in 2015.
Iran was Turkey's third largest export market in 2012. In fact, Iranian media said, Turkey exports more than 20,000 products to Iran, among them gold and silver.
The gold trade boomed in 2012 when Ankara was paying for Iranian natural gas and oil imports with Turkish lira and Tehran was using those deposits held in Turkey's state-run Halkbank to buy gold.
Some of the gold was held inside Turkey at the peak of the trade while some was taken to Dubai by couriers to be sold for foreign currency that was urgently needed by Iran as sanctions increasingly cut off access.
But the gold trade dried up under the chokehold of sanctions on precious metals transactions with Iran, with Halkbank also unable to process oil payments by other countries back to Tehran.
The United States has been unhappy over continued trade with Iran by its Turkish ally sidestepping the sanctions regime, and has blacklisted some Turkish firms involved.
U.S. Treasury Under Secretary David Cohen, who visited Turkey just before Erdogan's Iran trip, warned the Turkish government against any rapid improvement of trade and economic links with the Islamic Republic before a final nuclear agreement is struck, according to Turkish media.
"Businesses interested in engaging in Iran really should hold off. The day may come when Iran is open for business, but the day is not today," Zaman newspaper quoted Cohen as saying. (Editing by Mark Heinrich)