President Recep Tayyip Erdogan has said Turkey is determined to eliminate threats in northern Syria.
He added that the attack by Kurdish YPG militants which killed two Turkish police officers was “the final straw”.
“We have no patience left regarding some regions in Syria which have the quality of being the source of attacks on our country,” Mr Erdogan said in a news conference following a cabinet meeting.
“We are determined to eliminate the threats originating from here either with the active forces there or by our own means."
The officers were killed on Sunday in northern Syria's Azaz region. Turkey said the guided missile attack was launched by the YPG from the Tal Rifaat region, according to the Interior Ministry.
Separately, ammunition that landed in two separate areas caused explosions in the southern Gaziantep province's Karkamis district, across the border from Syria's Jarablus, the governor's office said.
A third piece of ammunition landed within Jarablus, it said, adding it was believed to be launched from a region controlled by the YPG, the US-backed Kurdish militants that Ankara considers a terrorist organisation.
“The latest attack on our police and the harassment that targets our soil are the final straw,” Mr Erdogan said.
Azaz and Jarablus have been under the control of rebels backed by Turkey since Ankara's first incursion into Syria in 2016, in an operation that aimed to drive away ISIS militants and the Syrian Kurdish YPG militia from its border with Syria.
Ankara has launched two other cross-border operations in Syria against the YPG, one of which targeted the Afrin region.
A car bomb also killed four people and wounded six in Afrin on Monday, local sources said.