David Cameron has promised to "fight" for Turkey's membership of the European Union, saying he is "angry" at the slow pace of negotiations.
On his first visit as prime minister, he said the country could become a "great European power", helping build links with the Middle East.
He compared hostility to the membership bid in some parts of the EU with the way the UK's entry was once regarded.
After his visit to Turkey, Mr Cameron will travel on to India.
He will be joined by a host of British business leaders as he seeks to boost trade links with one of the world's fastest growing economies.
Mr Cameron was expected to agree a new strategic partnership with Turkish Prime Minister Tayyip Erdogan during his visit.
In a speech at the Turkish parliament in Ankara, Mr Cameron said he wanted to "pave the road" for Turkey to join the EU, saying the country was "vital for our economy, vital for our security and vital for our diplomacy".
A European Union without Turkey at its heart was "not stronger but weaker... not more secure but less... not richer but poorer".
Mr Cameron added: "I'm here to make the case for Turkey's membership of the EU. And to fight for it."
At a joint press conference with Turkish Prime Minister Recep Tayyip Erdogan, Mr Cameron suggested the UK would impose provisional restrictions - as with Bulgarians and Romanians after they joined - on the right of Turkish people to live and work in the UK after it joined the EU.
But the rapid rate of Turkey's economic growth would make any restrictions unncessary in decades to come, he added.
He said: "One of the effects here is that [as] economies grow and become more evolved, the pressure and flow [of people] between countries isn't so great."
Referring to former French President General Charles de Gaulle's efforts to block British membership of the EU's predecessor, the European Economic Community, in the 1960s, Mr Cameron said in his speech: "We know what it's like to be shut out of the club. But we also know that these things can change.
"When I think about what Turkey has done to defend Europe as a Nato ally, and what Turkey is doing today in Afghanistan, alongside our European allies, it makes me angry that your progress towards EU membership can be frustrated in the way it has been.
"My view is clear. I believe it is just wrong to say that Turkey can guard the camp but not be allowed to sit in the tent.
"So I will remain your strongest possible advocate for EU membership and greater influence at the top table of European diplomacy."
Turkey opened accession negotiations with the EU in 2005 but is considered very unlikely to join in the next 10 years, partly because of opposition from countries such as France.
Its refusal to recognise EU member Cyprus, growing support for pro-Islamic parties on the mainland and the treatment of the Kurdish minority in the country all remain potential stumbling blocks.
Since 2005, only 11 out of 35 "negotiating chapters" relating to accession talks have been opened for discussion and only one has been "provisionally closed".
Mr Cameron said those who opposed EU membership were driven by protectionism, narrow nationalism or prejudice.
"Those who wilfully misunderstand Islam, they see no difference between real Islam and the distorted version of the extremists. They think the problem is Islam itself. And they think the values of Islam can just never be compatible with the values of other religions, societies or cultures."
He said: "All of these arguments are just plain wrong. And as a new government in Britain, I want us to be at the forefront of an international effort to defeat them."
While praising Turkey's secular and democratic traditions, Mr Cameron stressed that Turkey must continue to push forward "aggressively" with economic and political reform to maintain momentum towards EU membership.
He said the country had a "unique influence" in helping to build a stable Afghanistan through political and economic co-operation and fostering understanding between Israel and the Arab world.
Mr Cameron said the Israeli inquiry into the attack on the Gaza flotilla had to be swift, transparent and rigorous - and said the situation in the Palestinian territory had to change.
"Humanitarian goods and people must flow in both directions. Gaza can not and must not be allowed to remain a prison camp," he said.
"Hopefully, we move in the coming weeks to direct talks between Israel and the Palestinians so it's Turkey that can make the case for peace and Turkey that can help to press the parties to come together, and point the way to a just and viable solution."
He also delivered a firm message to Iran, against whom Turkey opposes further sanctions, saying there was no other "logic" to Tehran's uranium enrichment programme than to produce a bomb.
"So we need Turkey's help now in making it clear to Iran just how serious we are about engaging fully with the international community," Mr Cameron said.