Merlin Entertainments said incidents in Manchester and London have dented domestic demand, and they are "cautious" on the levels of overseas visitors in the coming months.
Merlin's LEGOLAND Parks and Resort Theme Parks operating groups have also been affected by the terrorist attacks and subsequent heightened security measures.
It said this had continued in the immediate aftermath to the Westminster attack.
However, Merlin also said that visits by foreign tourists to its London sites had been boosted by the weakness of the pound - making their holidays to the United Kingdom cheaper.
"The impact of recent terror attacks on our London attractions is unclear at this stage", said Nick Varney, Merlin's chief executive.
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He said: "What is clear, however, is that London has bounced back before, and will do again".
Merlin shares were the biggest faller in early trading on Tuesday, down 3.5%. "London is very much open for business, welcoming visitors from the United Kingdom and from around the world to this exciting and vibrant city".
As it expanded its business globally, Merlin said it has been trading in line with expectations in the year to date.
As part of the development, Merlin has this year opened 250 accommodation rooms in Legoland Florida and Legoland Billund.
"Merlin has a diverse portfolio of global brands with over 70% of 2016 profits from outside the United Kingdom and this proportion will only grow over time as the company we continue to invest internationally. I remain confident in the company's underlying growth prospects", said Varney.
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