When she was asked about Mr Trump's claims in an interview with USA Today, Ms Conway suggested the surveillance may have involved far more than wiretapping.
She said: “What I can say is there are many ways to surveil each other.
“You can surveil someone through their phones, certainly through their television sets — any number of different ways.”
She claimed surveillance could be conducted with "microwaves that turn into cameras," and added: “We know this is a fact of modern life.”
The unsubstantiated claim comes after Mr Trump's evidence-free accusation he was wiretapped by Mr Obama during the presidential election, a charge the former president denied.
FBI director James Comey has privately urged the Justice Department to dispute Mr Trump's claim, but has not come forward to do so himself.
A senior congressional aide said the House intelligence committee asked the Trump administration to provide evidence the phones were tapped, a request reinforced by an influential Republican, Senator John McCain.
"I think the president has one of two choices: either retract or to provide the information that the American people deserve, because, if his predecessor violated the law, President Obama violated the law, we have got a serious issue here, to say the least," the Arizona senator said.
Mr Obama's director of national intelligence, James Clapper, has said nothing matching Mr Trump's claims had taken place.
Regardless, Mr Trump has asked Congress to investigate.
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