* Deals illustrate thaw in Ankara's relations with EU
* Erdogan says Turkey will not be a burden on bloc
* Ankara began EU accession negotiations in 2005 (Adds Erdogan quotes, background)
By Ayla Jean Yackley and Tulay Karadeniz
ANKARA, Dec 16 (Reuters) - Turkey and the European Union signed an agreement on Monday allowing EU governments to send back illegal immigrants crossing into Europe from Turkey in a move highlighting a thaw in relations with the 28-member bloc.
Turkey lies on a major route for illegal migration into Europe from Africa and the Middle East, and some in western Europe fear Turkish membership would widen the bloc's borders too far to the fringes of Iran, Iraq and Syria.
At a ceremony in Ankara, Turkish Foreign Minister Ahmet Davutoglu and EU Home Affairs Commissioner Cecilia Malmstrom also signed an accord to enter into discussions on dropping visa requirements for Turks visiting Europe.
The agreements are a fresh sign of improved ties between Ankara and the EU after they began a new round of membership talks last month following a three-year hiatus.
"A new process in Turkish-EU relations is beginning," Prime Minister Tayyip Erdogan said in a speech at the ceremony.
"With our signatures today, the European doors are being opened for visa-free travel by Turkish citizens."
Turkey began negotiations to join the EU in 2005, 18 years after applying. But a series of political obstacles, notably over the divided island of Cyprus, and resistance to Turkish membership in Germany and France, have slowed progress.
Negotiations had most recently been delayed by the bloc in protest over a Turkish crackdown on anti-government demonstrations over the summer.
Malmstrom said she hoped the readmission agreement would be ratified by the two sides without delay and substantial progress would soon be made in the visa liberalisation dialogue, although she declined to be drawn on a timeframe.
"This autumn there has been a new launch in relations ... (The agreement) can contribute to building trust and can lead to new types of co-operation," she told Reuters.
Turkey has provisionally closed just one of 35 chapters it must negotiate with the EU to bring its laws into line with the 28-nation bloc's standards. It has 13 other chapters open.
Erdogan rejected what he said was an impression in Europe that Turks would surge into the EU if requirements were lifted.
"If EU visas are abolished, neither Turkey nor EU member countries will experience the slightest problem ... We are coming to take on a burden, not to be a burden," he said.
Talks on the "readmission agreement" to send back illegal immigrants had been stalled for years, largely due to Turkish distrust over the EU's willingness to ease visa rules.
Malmstrom said the number of irregular migrants travelling into Europe from Turkey had been steadily falling to around 20,000 this year from more than three times that number in 2010, partly due to better border co-operation with Greece and the economic crisis making Europe less appealing.
(Writing by Daren Butler; Editing by Nick Tattersall and Ralph Boulton)