Mishaal told AFP before Friday's meeting in Moscow with Russian officials that Hamas, which refuses to recognise the state of Israel, was ready to "move forward" in its relations with that country.
"Hamas is fully ready to go forward as much as this is possible. Everything now depends on Israel's policies," he said.
Sergei Lavrov, the Russian foreign minister, said on Friday that Moscow counted on Hamas, which is preparing for power after its January election victory, to implement previous Palestinian Authority agreements with Israel.
"We count on Hamas, as the leading political force in the parliament and future government, to contribute to the full and all-encompassing implementation of all previous agreements," he told Mishaal, Hamas' exiled politburo chief.
Ismail Haniya, Hamas' prime minister-designate, said in Gaza City: "We are optimistic (about the visit) and we are waiting for Russia to assume fully its political role in the Middle East."
On Friday, after the Palestinian delegation arrived in Moscow, Muhammad Nazzal, a senior Hamas official accompanying Mishaal, said "the issue of recognition is a done issue. We are not going to recognise Israel".
Lavrov: We count on Hamas to
implement all previous accords
Russia has said that - in the talks on Friday - it will endorse the view of fellow patrons of the "road map" to Israeli-Palestinian coexistence that Hamas must recognise Israel, renounce violence and accept past peace accords.
The pledge helped to quell concern in Israel, which sees Hamas as a spearhead of a more than five-year-old Palestinian uprising (intifada).
Hamas regards the visit as a chance to push its position on the Western stage after winning support in the developing world.
Mishaal said: "Our visit to Moscow is a very important step for achieving a breakthrough in our international position."
He added that "this is a visit that has no conditions. We will listen to the position of Russian officials and we will clarify our own position."
In an interview with NTV television in Syria on Thursday, Mishaal said: "Our people want simple things: to be free and to have sovereignty. All this is impossible without an end to the occupation."
Hamas, whose charter calls for resistance to the occupation and the return of all Palestinian land, has been responsible for several bombings during the intifada, but has largely abided by a truce declared last year which paved the way for Israel's withdrawal from Gaza.
While so far ruling out permanent coexistence, Hamas has said it can accept a long-term ceasefire if Israel also quits all of the occupied West Bank and accepts an influx of Palestinian war refugees.
Hamas is under pressure to make
changes in its hardline charter
By inviting Hamas to Moscow, Vladimir Putin, Russia's president, is seen as trying to boost his country's diplomatic influence in the Middle East, on the wane since the Soviet Union fell.
Russian analysts, however, were sceptical of Moscow's ability to persuade Hamas, and predicted that the talks would lead to nowhere.
Fyodor Lukyanov, editor of the foreign policy magazine Russia in Global Affairs, said: "Hamas won't listen to Russia because Moscow has no real levers of influence over them.
"This is not the time of the Soviet Union, when we had real clout in the region."