"Egypt will not hesitate in defending its brothers in the Gulf if they were to face a direct threat," said Sisi.
The president added that the Egyptian army was "the army of all Arabs", and the offer would not contradict with Egypt's commitment not to interfere in the affairs of other nations.
Egypt receives billions of dollars in aid from Gulf nations and is part of the Saudi-led military campaign in Yemen, but has so far not committed ground troops to the campaign - a move which has been severely criticised in Gulf capitals.
Sisi recently extended his country's involvement in the Saudi-led coalition until February 2017.
But, earlier this week, Egyptian Foreign Minister Sameh Shoukry said Egypt would not join Saudi Arabia in any military operation in Syria, after Riyadh expressed readiness to send ground troops into the war-torn country.
Sisi reiterated the point made by his foreign minister in front of his Kuwaiti guests.
"The Egyptian position regarding this [Syrian] crisis is clear and has not changed," said Sisi.
"It is based on not interfering in Syrian affairs, respecting the will of its population, combatting terrorism and extreme elements and working to find a political solution to the crisis that protects the unity of Syrian territories and paves the way for reconstruction."
Sisi's position on Syria is seen as a major point of disagreement between him and his Gulf allies, upon whom he increasingly depends to keep his administration afloat.