(CNN) The Kremlin has pushed back against Turkey's allegations that a movement led by exiled cleric Fethullah Gulen was behind the assassination of Russia's ambassador to Ankara.

"We need to wait for results of a joint investigative group. You shouldn't be in a rush to make conclusions until the investigation identifies who was behind the murder of our ambassador," Kremlin spokesman Dimitri Peskov said Wednesday.

Russian and Turkish investigators are trying to learn more about the assassination of Russian ambassador Andrey Karlov, who was gunned down Monday evening while speaking at the opening of an art exhibit in Turkey's capital.

Turkish President Recep Tayyip Erdogan said Wednesday that there are "leads regarding the foreign connections" of the shooter, who has been identified as Mevlut Mert Altintas.

"The FETO connection of Russian Ambassador Karlov's assassin is obvious. He is a member of FETO; there is no need to hide this," Erdogan said on Turkish television, using the shorthand name for Fethullah Terrorist Organization, which is what the Turkish government calls Gulen's movement.

Photos: Shooting unfolds in front of photographer Andrey Karlov, the Russian ambassador to Turkey, speaks at the opening ceremony of a photo exhibit in Ankara, Turkey, on Monday, December 19. Moments later, he was fatally shot. Associated Press photographer Burhan Ozbilici was at the event and watched the assassination unfold. Hide Caption 1 of 7 Photos: Shooting unfolds in front of photographer The man holds his gun up after shooting Karlov. The attack occurred at the Cagdas Sanat Merkezi modern arts center in Ankara. Turkish Interior Minister Suleyman Soylu said in a news conference that the gunman was Mevlut Mert Altintas, a Turkish police officer. Hide Caption 2 of 7 Photos: Shooting unfolds in front of photographer Karlov's body lies on the floor as the gunman stands nearby. Hide Caption 3 of 7 Photos: Shooting unfolds in front of photographer The gunman gestures near the body of Karlov. In a video circulating on social media, the shooter is heard shouting, "Allahu akbar (God is greatest). Do not forget Aleppo! Do not forget Syria! Do not forget Aleppo! Do not forget Syria!" Russia has been instrumental in helping Syrian President Bashar al-Assad's regime in its push to retake the eastern sector of Aleppo, which had been held by rebels for nearly four years. Russia is also the most powerful ally of Assad's regime and has carried out airstrikes since September 2015 to prop up the embattled leader. Hide Caption 4 of 7 Photos: Shooting unfolds in front of photographer People cower after Karlov was shot. "Get back! Get back!" the gunman could be heard shouting in Turkish.

Hide Caption 5 of 7 Photos: Shooting unfolds in front of photographer The gunman stands near the body of Karlov. "Only death will remove me from here. Everyone who has taken part in this oppression will one by one pay for it," he said in the video. Hide Caption 6 of 7 Photos: Shooting unfolds in front of photographer Turkey's official Anadolu news agency reported that the gunman had been neutralized. But it was not immediately clear whether the attacker was killed or captured by police. Later, Turkey's Interior Ministry said Altintas had been killed. Hide Caption 7 of 7

Gulen , a former ally and current rival of Erdogan, has been in self-imposed exile in Pennsylvania since 1999. He leads a popular movement called Hizmet, which includes hundreds of schools, hospitals and relief agencies.

But Turkey's government accuses the movement of being behind a failed coup in July -- an allegation Gulen denies. Ankara has demanded that the United States extradite the cleric.

Meanwhile, Russian President Vladimir Putin will delay his annual news conference in order to pay his respects to the slain ambassador, whose funeral will be held Thursday, Russian state-run news agency Sputnik reported.

Shooter: 'Don't forget Aleppo!'

Police say Altintas was the 22-year-old Turkish police officer standing behind Karlov while the ambassador was speaking at the Cagdas Sanat Merkezi modern arts center in Ankara.

Altintas, dressed in a dark suit and tie, fired several shots at Karlov , shouting, "God is greatest! Do not forget Aleppo! Do not forget Syria! Do not forget Aleppo! Do not forget Syria!"

Turkish security forces eventually killed Altintas, Turkey's Interior Ministry said.

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Altintas was not on police duty at the time, having taken sick leave Monday, Turkish state news agency Anadolu reported. Investigators are checking whether he'd had any connection with Russian Embassy staff, according to Anadolu.

Officials with Ankara's Cankaya district, which operates the art center, said Wednesday that Altintas bypassed an X-ray machine at the center by showing his police identification. As a police officer, Altintas would have been permitted to carry a firearm at all times.

"It was found out that the attacker was warned by the security staff when he didn't go through the X-ray, and upon this (the attacker) entered by showing his official police ID," the district's council said.

12 people detained

Turkish authorities have detained 12 people in the investigation of Monday's shooting, Anadolu reported Wednesday.

Emergency vehicles respond to the shooting of the Russian ambassador in Ankara.

Anadolu also reported that books about al Qaeda and Gulen's movement were found after a search of Altintas' home.

The 12 detainees include a man who police say led a network affiliated with Gulen at the Izmir-based Rustu Unsal Police Academy, from which Altintas graduated, Anadolu reported.

The detainees also include Altintas' parents, his sister, two other relatives, his roommate, an unidentified suspect and four police officers who were hired during the same term as Altintas, according to Anadolu.

A 13th person, Altintas' uncle, was released under "judicial control," or bail-like conditions, Anadolu quoted security sources as saying.

According to Anadolu, the uncle was a former senior executive at a private school connected with Gulen . The school was shut down after the July coup attempt.

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The failed coup triggered a wave of arrests and detentions of those suspected of any involvement. Turkey also suspended or dismissed tens of thousands of people in various institutions who were perceived as being opposed to the government.

That included the suspensions of more than 12,000 police officers who were accused of having links to Gulen.

Putin: Shooting tried to undermine Russia-Turkey relations

Putin said Karlov's killing was a clear provocation aimed at undermining not just the normalization of Russian-Turkish relations but also a "peace process in Syria" promoted by Russia , Turkey, Iran and other countries.

Marina Davydova Karlova bids farewell Tuesday to her husband, the late Russian envoy, in Ankara.

"The only response we should offer to this murder is stepping up our fight against terror, and the criminals will feel the heat," Putin said in televised remarks. An 18-strong investigative team of Russia's special agencies arrived in Turkey to help authorities with their inquiries.

The Ankara Police Department has devoted 120 people, including anti-terror personnel and interpreters, to work with the Russian team, Anadolu reported.

Erdogan echoed Putin's sentiments, saying, "The Russian government and the Turkish republic have the will to not fall into that provocation."

Karlov's assassination came at a time of improving relations between the two countries, which hit an all-time low after Turkish forces shot a Russian warplane out of the sky near the Syrian border in November 2015.

Russia slapped a raft of sanctions on Turkey after the deadly incident, hurting Turkish exports and damaging its tourism industry.

The relationship began to thaw in June when Erdogan wrote a letter expressing "regret" to the dead pilot's family. After Erdogan faced down the attempted military coup in July, Putin was among the first world leaders to call and offer his support.

Karlov's body arrived in Moscow late Tuesday. The ambassador was honored at a ceremony attended by Russia's foreign minister, the Turkish foreign minister and Karlov's widow, according to Russia's Foreign Ministry.

Roles of Russia and Turkey in Syria

Aleppo is the northern Syrian city that has been contested between rebels and Syrian government forces in the country's years-long civil war. Russia, the most powerful ally of the regime of Syrian President Bashar al-Assad, began airstrikes in Aleppo and elsewhere in Syria last year to prop up the embattled leader.

The Syrian regime is on the verge of retaking all of Aleppo from rebel groups who have controlled parts of the city since 2012. Moscow has carried out airstrikes since September 2015 to prop up Assad.

Human rights groups and other countries have denounced Russia over its backing of the Syrian leader.

As one of the five permanent members of the UN Security Council, Russia has used its veto powers to block certain proposed political solutions to end the war.

The bombardment in Syria has drawn criticism from Western powers, with President Barack Obama last week accusing Russia of slaughtering civilians in Aleppo in concert with the Assad regime. Moscow has recently tried to distance itself from the assault in eastern Aleppo.

Turkey's involvement in Syria is complicated. On one hand, the Turks are eager to help eradicate ISIS. On the other, Ankara is opposed to a group of Kurdish fighters battling ISIS inside Syria, saying those Kurds are linked to Turkey's own Kurdish insurgents -- the outlawed Kurdistan Workers' Party, or PKK, which Turkey has been fighting for years.

Turkey fears that an entrenched Kurdish area in Syria would fuel momentum for an independent Kurdish state that could claim Turkish territory.

Meanwhile, the United States supports Kurdish groups in both Syria and Iraq as critical partners in the battle against ISIS.