(adds quotes, background, U.S. reaction)

BANJA LUKA, Bosnia, Feb 22 (Reuters) - Bosnian Serb lawmakers have threatened to hold a referendum on secession from Bosnia if a majority of U.N. member states and the European Union recognise Kosovo's independence.

The parliament of the Serb Republic adopted a resolution late on Thursday branding Kosovo's declaration of independence an illegal act that violated Serbia's territorial integrity.

It warned that Kosovo's recognition by major powers was setting a new international precedent.

"The People's Assembly of Republika Srpska therefore considers that it has the right to determine its stance about its state and legal status through a direct vote by a referendum," it said in the resolution.

Bosnia is made up of the Serb Republic and the Muslim-Croat federation, a dual-entity state created by the Dayton accords that ended the 1992-95 war among Bosnian Serbs, Croats and Muslims.

Bosnian Serbs want to keep a high degree of autonomy and have closer links with Serbia. Muslims and Croats want a stronger state able to lead the country towards European Union membership.

Bosnian Serb Prime Minister Milorad Dodik told parliament there was no rush to break up the country.

"We are not adventurers and we do not plan to broach a decision about independence now," he said. "The referendum can be used only once, if we decide and when we decide it. It is no game."

But U.S. ambassador Charles English said there was no way any region could secede from the country whose "structures of self-determination" were defined by the Dayton accords.

"Talk about sovereignty of one entity is talk about something that does not exist. It is an irresponsible and unconstitutional concept," English told reporters in Sarajevo.

The resolution, adopted solely by the Serb MPs, warned that unless Bosnia's state institutions confirmed the Serb Republic's autonomy, as laid out in the 1995 Dayton peace accords, the Serb Republic would reconsider its status in the country.

Dodik called on the Bosnian Muslims and Croats to accept the Serb Republic as reality so that they all can live together.

"If there is no response, it will be a clear signal how they see us and we shall have to define a different policy," he said.

At a Belgrade protest rally against Kosovo's independence on Thursday, Dodik said: "We live in Bosnia but we look at Serbia."

The rally turned violent when several hundred protestors stormed the U.S. embassy, setting part of the building on fire.

The U.S. office in the Serb Republic capital Banja Luka was closed following violence on Thursday, when three policemen were seriously wounded trying to prevent protesters from breaking in. Nearly 30 protesters were detained, most of them minors. (additional reporting by Maja Zuvela) (Writing by Daria Sito-Sucic, editing by Giles Elgood)