* University rector was appointed by Erdogan
* More than 300 detained this week
* Erdogan says protestors are 'terrorists' (Updates with State Department comment)
By Ali Kucukgocmen, Ezgi Erkoyun and Tuvan Gumrukcu
ISTANBUL, Feb 3 (Reuters) - President Tayyip Erdogan said on Wednesday his government would not allow month-long demonstrations at a Turkish university to grow into anti-government protests similar to those in 2013, calling the protesters "terrorists".
Defying a government ban on demonstrations, students and teachers at Istanbul's Bogazici University have protested Erdogan's appointment of Melih Bulu, an academic and former political candidate, as rector.
They say the process was undemocratic and want him to resign, causing a nationwide debate over the government's reach and separate protests elsewhere. More than 250 people were detained in Istanbul this week and 69 others in Ankara.
The United States on Wednesday said it was "concerned" by the detentions of students and other demonstrators while condemning the anti-LGBTQI rhetoric around the protests. Turkey's interior minister on Tuesday called student protesters "LGBT deviants" on Twitter, prompting the social media platform to put a rare warning on his comment.
The unrest marks some of the largest demonstrations since 2013 when hundreds of thousands of people marched against government plans to build replica Ottoman barracks in Istanbul's Gezi Park.
"This country will not be run by terrorists. We will do whatever is needed to prevent this," Erdogan told members of his AK Party. He said young protestors lack Turkey's "national and spiritual values" and are members of terrorist groups.
"Are you students or terrorists trying to raid the rector's room?" Erdogan said. "This country will not again live a Gezi event in Taksim, will not allow it. We have not stood with terrorists and we will not."
Bulu said earlier he would not step down despite growing calls. "I am never thinking about resigning," Turkish media quoted him as telling reporters.
The main opposition party leader, Kemal Kilicdaroglu, has called for Bulu's resignation. Ankara Mayor Mansur Yavas urged Bulu in an open letter to "sacrifice" his position instead of "academic peace, youth and our future".
Bulu, who once applied to the AK Party to run for parliament, told broadcaster HaberTurk that the "crisis will be totally finished within six months."
U.S. State Department spokesman Ned Price said, that freedom of expression, "even speech that some may find uncomfortable, is a critical component of vibrant functioning democracy."
"The United States....stands shoulder to shoulder with all those fighting for their fundamental democratic freedoms," he said.
On Tuesday, academics again gathered on the Bogazici campus with their backs turned to the rector's building in protest and chanted "Melih Bulu resign," carrying signs reading "159," the number of those detained on Monday.
Students have shared images on social media of a picture displayed at the university that mixed LGBT symbols and Islam's holiest site, the Kaaba shrine in Mecca. The picture was condemned by Interior Minister Suleyman Soylu.
Erdogan said "there is no such thing" as LGBT. "This country is national and spiritual, and will continue to walk into the future as such," he said.
Furkan Dogramaci, 23, a Bogazici graduate last year, said a "lynching campaign" against the LGBT community was launched to thwart the protest's real aim. The government response aimed at "dividing, separating us and ending this movement," he said.
University student Enes Gozukucuk, 23, who was among protestors on Monday when police detained 51 people, said the protests were against Bulu's appointment not the government.
"We could have solved these issues amongst ourselves in the school. There was no need for violence from government forces," he said.
(Additional reporting by Humeyra Pamuk in Washington Writing by Jonathan Spicer; Editing by Dominic Evans and Alistair Bell)