Lavrov and other Russian officials have called on their countrymen in Turkey to stay indoors amid uncertainty about whether a military coup is taking place. However, relations appeared to be moving toward fix after Turkish President Recep Tayyip Erdogan issued an apology for the incident last month.
Military jets were flying at low altitude over the capital.
Meanwhile, Eken's live stream post on Facebook depicted the scenes at the time.
Turkish authorities have confirmed that in total, 161 people were killed as a result of the attempted coup, while 1,440 were injured.
As the popular tide turned against them, dozens of soldiers backing the coup surrendered on the Bosphorus Bridge in Istanbul they had held throughout the night, holding their hands above their heads as they were detained, TV footage showed.
He said that, as things stood, Turkey's cooperation in counter-terrorism efforts, in North Atlantic Treaty Organisation, on Syria and in countering Islamic State (ISIS) militant group had not been impaired.
Turkish Prime Minister Binali Yildirim said in Ankara on Saturday "the situation is completely under control".
In a statement on Saturday, the White House said President Obama "reiterated the United States' unwavering support for the democratically-elected, civilian Government of Turkey".
It appears not to have been backed by the most senior ranks of the military, and Turkey's main opposition parties quickly condemned the attempted overthrow of the government.
While Erdogan insisted the government was in control, some fighting appeared to continue into Saturday.
Zarif said in a tweet he was "deeply concerned about the crisis in Turkey".
Already authorities in Turkey removed 2,745 judges from duty following the attempted coup, reported broadcaster NTV, citing a decision by the High Council of Judges and Prosecutors (HSYK).
The Foreign Secretary, Boris Johnson, says he has spoken to his Turkish counterpart and underlined the UK's support for Turkey's democratically elected government.
Turkish Foreign Minister Mevlut Cavusoglu said Turkey demanded the "eight treacherous officers who fled to Greece by helicopter" be extradited.
The rebels struck on a weekend when the president was out of town at a holiday resort - but they failed to capture any of the ruling AK Party leaders or to shut down private television, mobile phone signals or social media networks.
Planes buzz Ankara and fire at the parliament building and a bomb explodes near the presidential palace. Turkey's renewed offensive against Kurdish militants - who seek more autonomy and are implacable foes of IS - has complicated the USA -led fight against the Islamic State group.
Gulen helped Erdogan consolidate his power in his early years of rule.
Turkey plays a key role in US -led efforts against the Islamic State group in Syria and Iraq. Regarded as an Islamist, Gulen was once an ally of Erdogan in Turkish politics before the two men and their respective power bases split.
"For more than 40 years, Fethullah Gulen and Hizmet participants have advocated for, and demonstrated their commitment to, peace and democracy", the Alliance for Shared Values said in a statement on Friday.