Four police officers were killed by a bomb on a road in Sirnak province and shortly after, gunmen opened fire on a military helicopter, killing a soldier.
Tension between the Turkish government and Kurdish militants has been rising.
One of the Istanbul attacks, on the US consulate, was carried out by two women and linked to a far-left group.
One of the female assailants in Monday’s attack was wounded and detained, and a rifle and other weaponry were seized, Istanbul’s governor said in a statement.
She is said to be a member of a radical Marxist group, the Revolutionary People’s Liberation Front (DHKP-C).
The DHKP-C previously claimed a 2013 suicide attack on the US embassy in the capital, Ankara.
The US consulate said in a tweet that it was closed until further notice.
In the other attack in Istanbul, on a police station in the district of Sultanbeyli, a car bomb was detonated, injuring 10 people, including three police officers.
Two suspected militants were killed in ensuing clashes with police and an injured police officer died later in hospital, reports say.
Following the attack on the military helicopter in Sirnak province, Turkish helicopters bombed Kurdistan Workers’ Party (PKK) targets in retaliation.
A ceasefire in the long-running conflict with the group appeared to disintegrate in July, when Turkey began bombing PKK camps in northern Iraq, at the same time as launching air strikes on IS militants.
PKK leader Cemil Bayik has accused Turkey of trying to protect ISIS by attacking Kurdish fighters.
Kurdish fighters – among them the PKK – have secured significant victories against ISIS militants in Syria and Iraq.
Turkey, like a number of Western countries, considers the PKK a terrorist organization.
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