Officials have been keen to stress that none of those visits were part of official royal duties.
At Thursday’s event, President Rivlin told Mr Quarrey: "During your term here, we will celebrate the centenary of the Balfour Declaration, which perhaps marks the beginning of the diplomatic relations between Israel and Britain.
“I greatly appreciate the words of Prime Minister David Cameron on the need to fight against fundamentalism – terror is terror, wherever it occurs.
“We are aware of the importance you place in creating confidence building measures in order to bring an end to the conflict in our region. We must first of all understand, and then make our neighbors understand that we are not doomed, but destined to live together.
“During your term here, we are looking forward, with your abilities and great experience, to receiving your assistance in building this confidence.”
Ambassador Quarrey emphasised his intention to further bilateral ties between the countries. He said: "A big part of my job over the next four years will be to develop the ties that we have in trade, investment, and in science and technology, which are of great benefit to both countries, and also is the best answer we have to those who call for boycotts of Israel."
He added: "As you say it is also vitally important that we work together against extremism in the region. David Cameron has spoken out very strongly on this, and the United Kingdom and Israel must be partners in this struggle against extremism.
“There is a great need for progress toward peace in the region - that need is very urgent, and we will do whatever is needed to support the difficult decisions required to achieve peace. I would also like to see more cultural collaboration between the UK and Israel and I hope to be able to give that a higher profile.
“Indeed, we are marking 400 years since the death of Shakespeare next year, and we look forward to marking that in Israel."
The event also welcomed four new ambassadors to Israel from Germany, Cyprus, Rwanda and the Seychelles.
