Addressing a rally of party workers here, he alleged that Modi insulted his "mentor" Advani despite Hinduism teaching how a "guru" was the most important person in an individual's life.
The Congress leader said he was the first person to pay a visit to former Prime Minister Vajpayee after his hospitalisation in the national capital yesterday.
Later in a tweet, he referred to Ekalavya, a character in the Hindu epic the Mahabharata, and said, "Ekalavya cut off his right thumb because his Guru demanded it. In the BJP, they cut down their own Gurus. Humiliating Vajpayeeji, Advaniji, Jaswant Singhji and their families is the Prime Minister's way of protecting Indian culture."
Addressing the party workers, he said Modi did not treat his guru (Advani) with respect even at official functions.
"Everybody knows who is the guru and mentor of Modi -- LK Advani. But the Prime Minister doesn't accord respect to him even at official functions. It is me who follows protocol and I am always with him (Advani) during (such) events," he said.
"Today I feel very sad for Advani ji. The Congress party has given him more respect than Modi ji has," he said.
Along with his tweet, Gandhi attached a video of an event where Modi is purportedly shown to have "ignored" Advani.
The Congress president said his party fought and defeated Advani in 2004 and 2009 parliamentary elections. "Now it is the Congress and our party's ideology which give respect to Advani," Rahul Gandhi said.
"We believe Vajpayee has contributed to the country," he added.