The Prime Minister described the accusations as quite shocking.
Unite officials have been accused of sending protesters to the homes of senior staff at Ineos, which owns Grangemouth.
Mr Cameron said people had a right to protest and that trade unions had a right to take industrial action.
"Those are rights and they're important rights, but no-one has a right to intimidate, nobody has a right to bully, nobody has a right to threaten people's families, no one has a right to threaten people in their homes and if these things have happened it is very serious and needs to be properly examined," he said.
"We shouldn't forget that the union action at Grangemouth was in danger of killing off an absolutely vital industry for Scotland and for the UK.
"So I think we need to have these actions properly investigated and I think also the Labour Party does need to investigate what has been happening with the Unite union not least because the person in question is still chairman of the Falkirk Labour Party."
Downing Street made clear last night that the Prime Minister thought that the inquiry should be carried out by Labour.
A spokesman for Ed Miliband accused the Prime Minister of being irresponsible and inflaming a difficult situation.
Mr Miliband said: "I condemn intimidatory tactics. It is not how industrial disputes should be conducted.
"This is true for unions just as it is true for employers."
Mr Cameron was also challenged to repeat comments he made in the House of Commons about the union official at the centre of the Grangemouth dispute.
David Cameron told MPs on Wednesday that Stephen Deans of Unite was a rogue operator, who nearly brought the Scottish petrochemical industry to its knees.
Mr Deans resigned quit his job at the Ineos plant at Grangemouth on Monday.
He was alleged to have used work time for local Labour Party business rather than legitimate trade union activity in his role as Unite convener at the plant.
Mr Deans is expected to be ousted as chairman of his local Labour Party this weekend.
Members of the Falkirk West Constituency Labour Party are expected to bring a motion of no confidence in his leadership on Sunday.
Len McCluskey, general secretary of Unite, said: "The Bullingdon bully who used parliamentary privilege to hound a decent trade unionist yesterday should not be lecturing others.
"He should make those comments outside of the Commons and then see what the courts make of them."