House of Representatives Foreign Affairs Committee head Michael McCaul told reporters of the alleged warning.
Israeli PM Benjamin Netanyahu described the reports as "absolutely false".
Israeli intelligence services are under scrutiny for their failure to prevent the deadliest attack by Palestinian militants in Israel's 75-year history.
"We know that Egypt has warned the Israelis three days prior that an event like this could happen," Mr McCaul told reporters following a closed-door intelligence briefing on Wednesday for lawmakers about the Middle East crisis, according to AFP news agency.
"I don't want to get too much into classified, but a warning was given," the Texas Republican added. "I think the question was at what level."
Egypt - which controls who crosses its border with Gaza - often serves as a mediator between Israel and Hamas.
More than 1,500 militants stormed through the Gaza security barrier in a co-ordinated land, air and sea attack on Saturday.
The death toll in Israel from the Hamas attacks has reached 1,200. More than 1,000 people have been killed by Israeli air strikes on Gaza.
Israel has been pounding Hamas targets in Gaza in response, while residents of the territory say they have no mains electricity after their only power station ran out of fuel.
Hamas has, meanwhile, condemned US President Joe Biden's remarks on Tuesday saying Israel had a duty to respond to the attacks, which he called an "act of sheer evil".
The Palestinian group said Mr Biden's remarks were "inflammatory" and aimed to escalate tensions in the Gaza Strip.
In the wake of the Hamas attack, the US announced it was moving an aircraft carrier, ships and jets to the eastern Mediterranean, and that it would also give Israel additional equipment and ammunition.
An Egyptian intelligence official told the Associated Press news agency this week that Cairo had repeatedly warned the Israelis "something big" was being planned from Gaza.
"We have warned them an explosion of the situation is coming, and very soon, and it would be big. But they underestimated such warnings," said the official, who spoke on condition of anonymity.
The Cairo official said Israeli officials had played down the threat from Gaza, instead focusing on the West Bank.
Sir Alex Younger, who served as chief of the UK's foreign intelligence agency between 2014 and 2020, said Hamas fighters were able to carry out their attack on 7 October due to "institutional complacency" in Israel.
"It is my assumption - though I'm not on the inside - that there would be data breaking through that could have been interpreted differently and certainly would be with hindsight," he said.
He added that complacency could have been compounded by an over-reliance on technological means to monitor Gaza, leading to a false sense of security.
According to the Financial Times, quoting two unnamed officials familiar with the matter, there was no hard intelligence of a specific attack.
On Wednesday, Mr Netanyahu described any suggestion that Israel had received a specific warning in advance of the deadly incursion as "totally fake news".