Tui Group chief executive Fritz Joussen said the operator was well prepared for any issues resulting from the decision.
He added: "The EU without the UK is barley conceivable but we respect the democratic decision of the British people and trust the UK government will take all steps necessary to ensure economic and political stability and to ensure that British holidaymakers will not be affected by the UK´s decision to leave the EU.
"Tui Group has highly professional risk management processes which have taken into consideration all possible scenarios. We are well prepared and confident that Tui Group as a truly global company will not be significantly affected by the decision.
"It remains to be seen how the decision will affect consumer sentiment.”
Aito chairman Derek Moore said: "Well, the people have spoken and now we face a new world, not least in the world of travel.
“Whether you were in favour of leave or remain, it’s now time to look forward and adjust to the new realities. It’s too soon to know exactly what effect leaving the EU will mean for our businesses; there may well be supplier cost, and thus customer price, implications and we will have to wait to see how airlines react to the situation.
“One thing is certain: whatever effect our new-found independence from Europe has on travel, it will affect us all equally so the playing field will still be a level one - at least to the degree that it always was. Hopefully now that the uncertainty of the referendum campaign days are behind us, people will book to travel abroad.
"It will be interesting to see what our relationship with the rest of Europe and further afield will now prove to be."
Chris Wright, managing director of Sunvil Group and GIC The Villa Collection, said: “Post Brexit, business will of course continue as normal at Sunvil - and bookings already made with us across our wide range of European and Latin American programmes will not be surcharged.
“Over the next few weeks and months, we will closely monitor the market situation and may make changes to our pricing strategy moving forward, if and when necessary. After 46 years in the travel industry, Sunvil has been through a considerable number of turbulent times before.
“The key message to our travel agency partners is for them to encourage consumers to book now to take advantage of the best prices possible.
"With prices at up to 50% off in Greece, it’s the best deal that their clients are likely to see this summer – and they are assured of a hugely warm welcome. Our Greek and other European partners in the travel industry rely hugely on the UK visitor market for their livelihoods, and it’s important for us to reassure them that it’s business as usual in the holiday arena, no matter what the headline news is.
"And holidays, after all, are vital for everyone’s wellbeing in this stressful 21st century life of ours.”
Meanwhile, Andrew Shelton, managing director of cheapflights.co.uk, added he believed the UK market was too vital to the continent for efforts not to be made to ensure a fair settlement.
He added: “The weeks of speculation about how a Brexit could change the price of travel to Europe has now become a question of how it will.
“Today’s Referendum result will throw the spotlight onto many benefits British travellers have taken for granted for years.
“Chief among these will be the European open skies agreements which created the environment for the budget airlines to thrive and which may now have to be renegotiated; a robust UK currency that has made the Eurozone so cheap to visit, the end of mobile data roaming charges, free healthcare within the EU and unlimited shopping allowances.
“However, holidaymakers shouldn’t assume that Brexit means all that will be lost.
“The UK travel market is vital to the economy of many European countries and regions. It will be in their interests to seek ways to maintain the status quo.
“We believe a lot of effort will be made in the coming months and years to ensure the UK cash cow isn’t put out to pasture.”
UKinbound chief executive Deirdre Wells said the industry contributes more than £22 billion per annum to the UK economy.
She added: “UKinbound feels the decision to leave the EU is disappointing and inevitably will have far-reaching consequences for our members.
“However, we have proved time and again that we are a resilient industry and the government must now work hard to secure a deal which supports our vibrant industry, which relies on the European Union for two-thirds of its business.
“The priority must now be to ensure that our members have the best possible environment in which to grow their business and to support them in welcoming visitors from all corners of the globe.”