* Protesters in Kharkiv seize, burn Ukrainian-language books
* Demonstrators smash way into Donetsk prosecutor's office
* Protests spread to southern cities (Adds details of Kharkiv protest)
By Lina Kushch
DONETSK, Ukraine, March 16 (Reuters) - Pro-Russian demonstrators in eastern Ukraine smashed their way into public buildings and burned Ukrainian-language books on Sunday in further protests following two deadly clashes in the region last week.
Protests, some several thousand strong, spread to Russian-speaking southern districts as Ukraine's Crimean peninsula, under the control of the Russian military for two weeks, voted in a referendum on joining Russia.
Violence in the east, where Russian-speakers are in the majority, has prompted warnings from Moscow that it is prepared to defend the rights of residents who disagree with the new pro-Western authorities in Kiev.
Clashes have broken out when rival rallies take place in proximity - pro-Russian groups against others backing the call by Ukraine's leaders for closer ties with the European Union.
The Kiev authorities, which have denounced the pro-Russian protests in the east as the work of "Kremlin agents", came to power after three months of often violent protests culminated in the removal of Moscow-backed president Viktor Yanukovich.
In Kharkiv, Reuters Television footage showed pro-Russian activists scaling an iron gate, smashing a van and breaking into the offices of a Ukrainian cultural centre. Two policemen stood nearby, examining the van.
The footage then showed young men seizing Ukrainian-language books, including a volume devoted to the 1932-1933 man-made famine in Soviet Ukraine, which killed from 7-10 million people.
"Do you see what they print here?" one activist said to another.
The activists then took the books into the street and set them alight in small bonfires, along with posters from the extreme-right wing Right Sector group.
Protesters moved through the city centre trailing banners dozens of metres (yards) in length bearing the Russian tricolour.
On Friday, two pro-Russian protesters were killed by buckshot after a confrontation outside the same cultural centre with activists from Right Sector.
PROTESTERS SMASH DOORS, WINDOWS
In Donetsk, the heart of the Donbass coalfield, where a pro-Ukrainian activist died in clashes on Thursday, 5,000 protesters roamed from a central square to several public buildings, smashing doors and windows as they went.
They massed for a time outside the local prosecutor's office before lines of riot police let them through and they pushed their way inside with poles and sticks. A small group clambered onto the roof, snatched away the blue and yellow Ukrainian flag and waved red-white-and-blue Russian standards.
Activists then moved on to the offices of the SBU security service, pushing their way inside for the second day running, before going to the headquarters of the Industrial Union of Donbass, owned by magnate and local Kiev-appointed governor Sergei Taruta.
Activists, many of them bearing the orange and black colours of the "St George ribbons" worn by Russian nationalists, were demanding the release of an activist who had briefly proclaimed himself "people's governor" of the region this month.
Several thousand pro-Russian demonstrators marched through the streets of the Black Sea port of Odessa.
Two cities held impromptu "referendums", banned by local courts, echoing the vote being conducted in Crimea.
In Luhansk, a coal-mining centre in northeastern Ukraine, organisers set up ballot boxes in a square asking voters five questions ranging from Kiev's new leaders to the creation of a federal state. A similar referendum was staged in the southern city of Mikolayiv. (Writing by Ron Popeski; Editing by Mark Heinrich and Robin Pomeroy)