At the same time, he said that a person's background does not determine his capabilities.
Responding to a question from students at the University of California, Berkeley, Gandhi said that he was "absolutely ready" to take up an executive responsibility if the party asked him to do so.
"Most parties in India have that problem So...Mr Akhilesh Yadav is a dynast. Mr Stalin (son of M Karunanidhi in DMK) is a dynast... Even Abhishek Bachchhan is a dynast. So that's how India runs. So don't get after me because that's how they India is run. By the way, last, I recall, Mr Ambanis are running the business. That's also going on in Infosys. So that's what happens in India," he said as he listed several prominent Indians born into famous families.
But, he said there were a large number of people in the Congress Party who were not from dynastic families.
"And I can name them in every state. There are also people who happen to have a father, or a grandmother or a great grandfather in politics. They do exist," he said.
"The real question is whether the person actually a capable and a sensitive person," he said.
Gandhi said around 2012, the Congress Party "stopped having conversations with the people".
He said this could be a problem for any party which is in power for 10 years.
"The vision that we laid out in 2004 was designed at best for a 10-year period. And it was pretty clear that the vision that we laid out in 2004 by the time we arrived in 2010-11 was not working anymore," the 47-year-old leader said.
"Somewhere around 2012, and I say this, a certain arrogance crept into the Congress party. And they stopped having that conversation."
When asked if he wanted to take up an executive role in the Congress Party, he responded by saying, "I am absolutely ready to do that".
However, he quickly left the decision on his party.
"We have an organisational election process that decides that. And that process is currently ongoing. So we have an internal system where we elect certain delegates who make that decision. So for me to say that that decision is mine that wouldn't be very fair.
"That's a decision that the Congress Party has to make and that's a process that's currently going on right now," he said.
He also said the BJP is implementing most of the programmes initiated during the Congress' rule.
"The central architecture they borrowed from us. But that architecture does not work. Because we know it. It stopped working," he said.
Gandhi said that Mahatma Gandhi's idea of non-violence in India is under attack today.
"The idea of non-violence is what has allowed this huge mass of people to rise up together."
He also criticised Prime Minister Narendra Modi's foreign policy.
"Whereas I completely agree with their positioning as far as the (ties with) the US are concerned, I think they're making India vulnerable because, if you look at Nepal, the Chinese are there. If you look at Burma the Chinese are there. If you look at Sri Lanka, the Chinese are there. If you look at Maldives, the Chinese are there," he said.
"So on basic direction (of the foreign policy) I agree... friendship with the United States, close bond with United States. But don't isolate India, because it gets dangerous," Gandhi said.