MOSCOW (Reuters) - Russian President Vladimir Putin phoned Iran's new interim president on Monday as Moscow made clear its desire to preserve and build on its deepening relationship with Tehran despite the sudden death of President Ebrahim Raisi.

The Kremlin said Putin expressed his condolences to interim president Mohammad Mokhber and to the whole Iranian people over Raisi's death in a helicopter crash, describing Raisi as a "reliable partner who made an invaluable personal contribution" to bilateral relations.

"Both sides emphasised their mutual desire to further consistently strengthen comprehensive Russian-Iranian interaction for the benefit of the peoples of the two countries," the Kremlin said in its readout of the Putin-Mokhber call.

State news agency RIA quoted Sergei Shoigu, secretary of Russia's Security Council, as saying Moscow could assist Iran in its investigation of the crash.

Since the state of the war in Ukraine, Russia has moved to strengthen its political, trade and military ties with Iran in a deepening relationship that the United States and Israel view with concern.

In January, Russia's Foreign Ministry said a new interstate treaty reflecting the "unprecedented upswing" in Russia-Iran ties was in the final stages of being agreed, and Putin and Raisi were expected to sign it soon.

Putin held five hours of talks with Raisi in the Kremlin in December and had spoken to him by phone in March and April, according to the Kremlin website.

Like North Korea, whose leader Kim Jong Un met Putin in Russia's far east last September, Iran is an avowed enemy of the United States and can provide Moscow with military hardware for its war in Ukraine, where Russia has made extensive use of Iranian drones.

Russia's deputy foreign minister said on Monday that Moscow expected all agreements with Iran to be implemented, state news agency RIA reported.

The Kremlin said that Putin had spoken to the Iranian ambassador to Moscow late on Sunday night following news of the helicopter crash.

Putin also sent his condolences to Supreme Leader Ayatollah Ali Khamenei.

"Seyed Ebrahim Raisi was an outstanding politician whose entire life was devoted to serving the Motherland," Putin said in his telegram.

"As a true friend of Russia, he made an invaluable personal contribution to the development of good neighborly relations between our countries and made great efforts to bring them to the level of strategic partnership."

(Reporting by Reuters, Writing by Mark Trevelyan; Editing by Guy Faulconbridge and Alison Williams)