The Queen spoke at a banquet hosted by Turkey's President Abdullah Gul
The Queen has described Turkey as "a bridge between East and West at a crucial time" during an official visit to the country.
She was speaking at a state banquet in Ankara, hosted by President Abdullah Gul and his wife Hayrunnisa.
Turkey had a "key role in promoting peace, political stability and economic development in some of the world's most unsettled areas", she said.
It is the Queen and Prince Philip's first visit to Turkey since 1971.
They are on a four-day state visit to the secular Muslim country to promote relations between it and the UK.
Earlier on Tuesday, the royal couple laid a wreath at the tomb of Mustafa Kemal Ataturk, the founder of modern-day Turkey.
The Queen called him "one of the greatest figures of modern history" and wrote in the mausoleum's visitors' book that it was an "honour" to pay her respects to "a much valued friend of the United Kingdom".
The President's wife Hayrunnisa defied the ban on wearing a headscarf
On Tuesday evening she gave a speech prepared by the Foreign Office at the presidential palace.
"For us, Turkey is as important now as it has ever been," she said.
"Turkey is uniquely positioned as a bridge between East and West at a crucial time for the European Union and the world in general."
The Queen wore a tiara and a white gown decorated with beads in the form of grape bunches.
She said to President Gul: "You are playing a key role in promoting peace, political stability and economic development in some of the world's most unsettled areas."
Britain is a strong supporter of Turkey's attempts to join the EU. The country became an official candidate in 1999 and entered formal accession negotiations in 2005.
At the banquet, President Gul thanked Britain for backing Turkey's bid.
"The United Kingdom has become one of our most loyal supporters in Turkey's march toward membership of the European Union," he said. "We are grateful for this unwavering and permanent support."
Mrs Gul wore a pink Islamic headscarf, despite a ban on them in public and governmental buildings.
Turkey's staunchly secular military is deeply opposed to headscarves being worn, while the ruling party, which has Islamic roots, believes religious symbols should be more openly accepted.
Highlights of the first day of the Queen's visit to Turkey
Later in the trip, the Queen and Duke of Edinburgh will visit the western city of Bursa and will tour a school in Istanbul which has links with UK students.
Turkey is seen as a key ally in the fight against terrorism. In recent years it has also led the International Security Assistance Force fighting the Taleban in Afghanistan.
The Prince of Wales and Duchess of Cornwall visited Turkey last November.
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