At least 24 Syrians were injured in the clashes and were brought across the border into the Turkish town of Ceylanpinar, according to an official in the Ceylanpinar mayor's office. The official said two of the injured men later died.
The official said the clashes erupted after a group of Kurds marched through Ras al-Ayn trying to hoist a flag of a Syrian Kurdish party.
He spoke on condition of anonymity in line with government rules that bar civil servants from speaking to reporters without prior authorization.
An Associated Press video journalist in Ceylanpinar heard gunfire and occasional shelling coming from the oil-rich city that at is predominantly Kurdish.
While the Assad regime has been isolated internationally for cracking down on dissent, Iran, Russia and China have backed Damascus during the conflict.
Tehran has started building a $10 billion natural gas pipeline to Syria as part of efforts to boost Iran's energy sector that has been battered by international sanctions.
Iran's semi-official Fars news agency said on Monday that the 1,500-kilometer (900-mile) pipeline will pass through Iraq before reaching Syria.
Iran began construction of the first phase of the project involving a 225-kilometer (140-mile) stretch at an estimated cost of $3 billion. The Fars report said the entire project is to be completed in the second half of 2013. The deal was signed between Iran, Iraq and Syria last July.
Associated Press writers Suzan Fraser in Ankara, Turkey and Maamoun Youssef in Cairo contributed to this report.