Turkey broke off diplomatic ties with the ex-Soviet republic in 1993 over Armenia's occupation of territory inside Azerbaijan, a regional Turkic-speaking ally of Ankara.
Ankara also angrily rejects Yerevan's claims that 1.5 million Armenians suffered genocide at the hands of Ottoman Turks during the first world war. Turkey says the Armenians were victims of a war which claimed even more Muslim Turkish lives.
But Erdogan, worried the genocide issue could harm Turkey's plans to start European Union (EU) entry talks in October, recently urged Armenia to help set up a commission of historians from many countries to establish what really happened.
Erdogan renewed that invitation in an interview with Milliyet newspaper, adding: "On the one hand, political relations could be established. On the other hand, work (on the archives) could continue. There is no Chinese Wall between us."
Armenian President Robert Kocharyan said this week he was ready to accept Erdogan's proposal for a joint commission to probe the genocide claims but he also said it was necessary to improve broader relations first.
Armenians say 1.5 million people
were killed by Ottoman Turks
Erdogan did not mention the possibility of restoring full
diplomatic relations, but his comments were the clearest sign yet that Turkey wants to mend fences with Armenia.
Some EU politicians, notably in France, home to western Europe's largest Armenian population, have said Turkey should recognise the alleged genocide of Armenians before being allowed to start accession negotiations with the wealthy bloc.
Historians must decide
But German Chancellor Gerhard Schroeder, who is due to pay an official visit to Turkey next week, ruled out any linkage
between the start of EU entry talks and the Armenian question.
"This (recognition of genocide) cannot be a precondition. This is about bilateral relations. It's for the historians to decide (what happened)," Schroeder told Turkey's NTV commercial television in an interview broadcast on Friday.
"It's very important for a nation to look at its history with an attitude of self-criticism"
He also praised Erdogan's offer to open up Turkey's archives on the period and his call for an international commission.
"It's very important for a nation to look at its history with an attitude of self-criticism," Schroeder added.
He said an expected vote in the German parliament in the coming weeks on a resolution concerning the alleged genocide should not upset relations between Ankara and Berlin.
Turkey has in the past threatened countries that do recognise the massacres as a genocide with diplomatic sanctions.
All countries aiming to join the EU are required to strive for good relations with their neighbours.
But despite the signs of a possible thaw in relations, diplomats say Turkey is unlikely to open its border with Armenia before Yerevan makes some gesture towards Azerbaijan in their long-running row over the breakaway region of Nagorno-Karabakh.