Syria said Sunday its troops intercepted anti-government rebels entering the country from neighboring Turkey as widespread fighting continued. The state-run Syrian Radio-and-TV said among the many successes enjoyed by the army on Saturday was an engagement near the Turkish border in Idleb province that sent the so-called terrorists fleeing back into Turkey. Turkey is providing shelter to an estimated 80,000 Syrian refugees and has been worried about being dragged into the bloody Syrian civil war. Damascus has consistently blamed the rebellion on \"terrorists\" supported by hostile foreign powers. Syrian Radio said the military inflicted heavy casualties on the rebels in clashes across the country, but did not supply exact figures. The battlefield reports could not be independently verified. The rebel Syrian Network for Human Rights said in a written statement it tallied 28 people killed in the fighting Sunday, including 10 in Idleb province. The new U.N. envoy to Syria met Saturday with President Bashar Assad in another attempt to ratchet the level of violence down. Assad told Lakhdar Brahimi his regime was committed to ending the conflict, but indicated foreign involvement in the process was not welcome. \"The success of the political work is linked to pressing the countries which fund and train the terrorists, confiscate weapons into Syria to stop such acts,\" the president said, according to a dispatch from the official SANA news agency. Brahimi, who recently replaced Kofi Annan as the chief U.N. and Arab League representative in Syria, told reporters he was still in the process of sorting out the current views of all parties, including regional and international, CNN said. \"We will set the plan that we will follow after listening to all internal, regional and international parties, hoping that such a plan will manage to open channels towards ending the crisis, and will be also accompanied by a clear strategy,\" Brahimi said.