By Ayla Jean Yackley

ISTANBUL (Reuters) - Five members of Turkey's security forces and five Kurdish militants were killed on Thursday in clashes in the southeast, where unrest has flared since the arrest this week of two popular mayors.

Two soldiers were killed in a clash near Hani, a town outside Diyarbakir, the region's biggest city, security sources said. A third died in a firefight near Cukurca near the Iraqi border, where five militants were also killed, they said.

A soldier was killed by a homemade explosive device in Bingol, 140 km (85 miles) north of Diyarbakir, and a member of a state-backed militia was killed in Batman province to the east.

Violence has escalated in the 15 months since the Kurdistan Workers Party (PKK) called off a two-year ceasefire, and the arrest of Diyarbakir Mayor Gultan Kisanak and her co-mayor Firat Anli late on Tuesday on terrorism charges has caused further resentment.

A lawmaker from the pro-Kurdish Peoples' Democratic Party (HDP) accused the government of blocking the internet throughout the mainly Kurdish southeast after the arrests.

President Tayyip Erdogan has said the removal of elected officials and civil servants accused of links to the PKK, listed as a terrorist group by Turkey, the United States and the European Union, is a vital part of the battle against it.

The U.S. State Department urged Turkey to "act with due restraint and respect for freedom of expression," spokesman John Kirby said late on Wednesday. "We would, again, note the importance of due process."

Senior officials in the European Union, which Turkey aspires to join, described the arrests as worrying.

FIRST FEMALE MAYOR

The local prosecutor said Kisanak, a member of parliament before becoming Diyarbakir's first female mayor in 2014, and Anli had given speeches sympathetic to the PKK, called for greater political autonomy for Turkey's estimated 16 million Kurds and incited violent protests in 2014.

Three city officials in Diyarbakir were also detained on Thursday after hanging a banner outside city hall in support of Kisanak and Anli, municipal officials said.

The banner had pictures of the two politicians and read: "Respect the will of the people, free our mayors". It was later removed by police.

A PKK leader urged Kurds to "rise up" in solidarity, reported Firat News Agency, a mouthpiece for the group.

Rebel commander Cemil Bayik said the importance of Diyarbakir, a city of 1.7 million people, meant actions against its elected officials were attacks on all Kurds, Firat said.

On Wednesday, the prosecutor invoked an emergency power to bar Kisanak and Anli from seeing a lawyer for five days.

HDP lawmaker Meral Danis Bestas submitted a parliamentary motion on Thursday asking why internet service in 12 provinces had been cut since 10.30 a.m. (0730 GMT) on Wednesday. A witness in Diyarbakir reported connectivity was restored at 5 p.m.

A spokeswoman at the state agency overseeing the internet was unable to comment on widespread reports of outages.

The autonomy-seeking PKK took up arms in 1984, and more than 40,000 people have died in the conflict since. Renewed violence since July 2015 has claimed thousands of lives.

(Additional reporting by Tuvan Gumrukcu; Editing by Daren Butler and Robin Pomeroy)