Hamas won elections in January 2006 but was shunned by the world powers, worsening a power struggle between the Palestinian factions.
Hamas presently controls the Gaza Strip, which it seized in 2007 after a series of deadly clashes with Fatah security forces. Fatah, led by Mahmoud Abbas, the Palestinian president, is based in the West Bank.
"Our rights of self-independence and self-rule must be recognised"
Hamas political chief
Meshaal said his group welcomed the "new tone of language" from Barack Obama, the US president, but he stressed that "we'll put this to test by deeds, not by words".
His comments came as Israel authorised hundreds of new settler homes in the occupied West Bank in the face of a construction freeze demanded by the US.
The settlements issue is a major obstacle in the stalled Israeli-Palestinian peace process and has caused a recent rift in Israel's relations with Washington.
Meshaal said "occupation must come to an end" and called for "withdarawal [of Israel] to 1967 borders".
"Our rights of self-independence and self-rule must be recognised," he said.
He warned against Israel's proposal to temporarily halt construction in exchange for normalisation with Arab countries, describing it as "dangerous".
On the question of a prisoner exchange, Meshaal said: "There has been a development with the German mediation taking place with the knowledge of Egypt and in co-ordination with us.
"We are still in the beginning; we haven't yet gotten into details or discussing the names, there is a still not a short path to go, which requires patience."
Egypt and Germany have been trying to broker the release of an Israeli soldier held by Hamas, in exchange for hundreds of Palestinians held in Israel's jails.
Gilad Shalit was captured by Hamas during a border raid in 2006.