Activists said fighting between Assad loyalists and rebels was concentrated in the northern edge of Latakia province.
The Britain-based Syrian Observatory for Human said government troops bombarded rebel positions with artillery as they tried to capture several strategic hilltops. Fighter jets also carried out several airstrikes.
State TV said army troops captured one of the hilltop positions known as the Observatory 45. It is a strategic post that is key to both sides because it has a commanding view of the contested surrounding mountains and green plains below.
It later showed footage of what it said were rebels killed in the area during the government offensive. Several bearded men in military uniforms lay dead, covered with blood, as government troops stood in the background.
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Opposition fighters from several conservative and hard-line Islamic groups, including the al-Qaeda-affiliated Nusra Front, launched their assault on the northern stretches of Latakia province along the Turkish frontier March 21.
So far, they have seized a border crossing, several villages and the predominantly Armenian-Christian town of Kassab. They've also gained control of an outlet to the sea for the first time since Syria's uprising began three years ago.
Government forces, backed by Lebanese Hezbollah fighters, have recently triumphed against the opposition along the border area with Lebanon, ousting rebels from their border strongholds inside Syria and cutting off supply routes from the neighboring country.
Syria's information minister lashed out at Turkey, accusing Ankara of sending foreign fighters across the border to fight Syrian government troops in Latakia.