* Khamenei values improving Russia ties-aide
* Putin, Velayati discuss Syria war
* Messages passed to Putin from Khamenei, Rouhani
* US pushes countries to cut Iran oil imports to zero
* Tehran working hard to keep oil output steady (Adds quote, detail)
By Parisa Hafezi
ANKARA, July 12 (Reuters) - The top adviser to Iran's Supreme Leader Ayatollah Ali Khamenei said his meeting with Russian President Vladimir Putin on Thursday had been "very constructive and friendly" and that Moscow would invest in the Iranian oil sector.
"Our leader (Khamenei) values improving ties with Russia as strategic partner ... This path will continue," the adviser, Ali Akbar Velayati, told Iranian state television from Moscow.
The Kremlin said Putin and Velayati discussed the situation in Syria and bilateral relations and Velayati had given Putin messages from Khamenei and from Iran's president Hassan Rouhani.
Russia, China and the big European powers say they still back a 2015 multinational nuclear deal with Iran, despite U.S. President Donald Trump's decision to pull out and to reimpose economic sanctions on Tehran that were lifted as part of the accord.
"Putin reiterated that Russia rejects America's decision to impose sanctions on Iran ... He said Russia will stand by Iran and will defend Tehran's rights," Velayati said.
Under the 2015 agreement, Iran strictly limited uranium enrichment capacity to satisfy the powers that it could not be used to develop atomic bombs. In exchange, Iran received relief from sanctions.
U.S. officials said in June they would push countries to reduce their Iranian oil imports to zero. However, U.S. Secretary of State Mike Pompeo said on Tuesday that Washington would consider requests from some countries to be exempted from sanctions it will put in effect in Nov. 4.
China and India are among the largest importers of Iran's oil, as well as Turkey and Iraq. In May, India's oil ministry asked refiners to prepare to limit imports of Iranian oil while Turkey said had no intention to halt its oil imports from Iran.
BOOSTING ENERGY TIES
Tehran has been pushing hard to hold output steady amid U.S. sanctions that are expected to hit its exports, pressuring other signatories of the deal to come up with a package of economic measures to salvage the deal.
"Putin said that Russia is prepared to continue its oil investment in Iran at the level of $50 billion. It means Russia is ready to invest this amount in Iran's oil sector," Velayati said.
"This is an important amount that can compensate for those companies that have left Iran (amid U.S. sanctions fear)," Velayati said, in a reference to a number of firms, wary of U.S. sanctions, that have already said they plan to pull out of Iran's market.
He said one of Russia's major oil companies has signed a $4 billion deal with Iran, which he said "will be implemented soon", without elaborating. "Two other major Russian oil companies, Rosneft and Gazprom, have started talks with Iran's Oil Ministry to sign contracts worth up to $10 billion," Velayati added.
Velayati said Iran and Russia shared the same view over Syria, where Tehran and Moscow as allies of Syrian President Bashar al-Assad have played decisive roles in turning the tide of war in his favour and in winding down some of the violence.
"Iran and Russia will continue to cooperate in Syria," Velayati said.
"Putin underlined the importance of political and defence cooperations between Iran and Russia in Syria. Soon the presidents of Iran, Russia and Turkey will attend a summit in Tehran," said Velayati, who is expected to visit China shortly. Trump and Putin are expected to discuss Iran's regional role and the Syrian conflict at a summit in Helsinki next Monday. (Additional reporting by Denis Pinchuk, Maria Kiselyova,Maria Tsvetkova in Moscow, Writing by Parisa Hafezi, Editing by Gareth Jones, William Maclean)
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