The overnight strikes killed "a number of civilians and soldiers, wounded others and caused significant damage to public and private property", the Syrian military said in a statement.

"The occupation of parts of Syrian territory by US forces cannot continue," it added, affirming the army's "determination to liberate all Syrian territory from terrorism and occupation".

The United States blamed Sunday's drone attack in Jordan on Iran-backed groups, but did not strike inside Iranian territory, with both Washington and Tehran seemingly keen to avoid all-out war.

The United States has some 900 troops in Syria and 2,500 in neighbouring Iraq as part of an international coalition against the Islamic State group, a jihadist organisation that once controlled swathes of both countries.

The Syrian foreign ministry said the strikes served to "inflame the conflict in the Middle East in an extremely dangerous way" and added "to the (US) record of violations of Syrian sovereignty" and territorial integrity.

Syria "condemns this blatant American violation and categorically rejects all the pretexts and lies used by the American administration to justify this attack", the ministry said in a statement.