"After several hours of waiting and multiple interrogations our two friends were permitted entry and my daughter and I were informed that we were denied entry after much discussion indirectly with the interior ministry."
Chomsky said the border officials were "very polite" as they "transmitted inquiries from the [Israeli] ministry of the interior".
He said that he believed he was denied entry was for two reasons.
"The government does not like the kind of things I say which puts them into the category of every other government in the world," he said.
"The second was that they seemed upset about the fact that I was taking an invitation from Birzeit and I had no plans of speaking to any Israeli universities as I've done many times in the past, but not this time."
However, a spokeswoman at the Israeli interior ministry, which controls the country's borders, said Chomsky had not been allowed to cross the border due to misunderstanding.
She said officials were trying to get clearance from the Israeli military, which controls access to the West Bank to allow Chomsky to enter.
"We are trying to contact the military to clear things up and if they have no objection we see no reason why he should not be allowed in," Sabine Hadad told the Reuters news agency.
Mustafa Barghouti, a Palestinian MP who had invited Chomsky to speak at the university's philosophy department, said the scholar had been detained at the border for five hours.
"This act shows the nature of the Israeli government that is against freedom of speech, particularly from such a noted international figure like Chomsky," Barghouti said.
Chomsky, 81, is a professor of linguistics at the US Massachusetts Institute of Technology and has frequently spoken out against Israel's occupation of Palestinian territories.