Turkish troops and tanks entered Syria on Sunday to push an offensive against Kurdish militia as rockets hit border towns in apparent retaliation and the United States urged Ankara to show restraint.

Turkey on Saturday launched operation “Olive Branch” seeking to oust from the Afrin region of northern Syria the peoples’ protection units (ypg) which Ankara considers a terror group.

In its first reaction to the offensive, the US state department urged Turkey Sunday “to exercise restraint and ensure that its military operations remain limited in scope and duration and scrupulous to avoid civilian casualties”.

“We call on all parties to remain focused on the central goal of defeating” is, state department spokeswoman heather Nauert said in a statement.

Turkish Prime Minister Binali Yildirim said troops crossed into YPG-controlled region in Syria at 0805 gmt, the Dogan news agency reported.

Thirty-two Turkish planes destroyed a total of 45 targets including ammunition dumps and refuges used by the Ypg on the second day of the operation, the Turkish army said.

Turkish troops were advancing alongside forces from the Ankara-backed rebel free Syrian Army (Fsa) and were already five kilometres inside Syria, state media said.

Foreign Minister Mevlut Cavusoglu said in televised comments several villages had already been taken in the advance.