Turkey has said it is ready to build "political" relations with Armenia while experts investigate Yerevan's claims of a World War I "genocide".
Mr Erdogan is pushing hard to get Turkey into the EU
Turkey does not have diplomatic ties with neighbouring Armenia, amid a row over the mass killings of Armenians by Ottoman Turks in 1915-1917.
Turkish Prime Minister Recep Tayyip Erdogan said "political relations could be established" during joint studies.
Armenia has cautiously welcomed the offer of a joint investigation.
On Tuesday, Armenian President Robert Kocharyan said he was ready to accept Mr Erdogan's proposal for a joint commission to probe the killings - but demanded a normalisation of relations first.
Mr Erdogan told Turkey's Milliyet newspaper that the establishment of formal diplomatic relations would depend on Armenia showing "sincerity" towards undertaking a joint investigation.
Armenia wants Turkey to admit the killings were "genocide"
Turkey shut its border with Armenia in 1993, angry at the Armenian separatist forces fighting for independence from Azerbaijan in the disputed territory of Nagorno-Karabakh.
Armenia alleges that the Young Turks, the dominant party in the Ottoman Empire in 1915, systematically arranged the deportation and killing of 1.5 million Armenians.
Turkey says up to 300,000 Armenians and at least as many Turks died during civil strife in eastern Turkey during World War I, but angrily rejects the allegation of a planned "genocide" of Armenians.
Some EU politicians want Turkey to recognise the killings as "genocide" before Ankara is allowed to open talks on EU accession.