At a news conference, senior Hamas figures in Gaza called for "the announcement of a precise date for presidential and legislative elections."
First deputy speaker of parliament Ahmed Bahar said Hamas and rival Palestinian factions should work to achieve reconciliation "and to close the gaps opened by years of political division."
Palestinian elections have not been held in a decade due to the bitter split between Hamas, which rules the Gaza Strip, and the West Bank-based Fatah faction led by Palestinian president Mahmud Abbas.
The elections never materialised, with the two sides blaming each other.
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Bahar welcomed the talks due to take place in the Qatari capital.
The Palestinian parliament has not met since 2007, the year Hamas seized the Gaza Strip by force and drove out Fatah from the enclave buoyed by its 2006 election victory.
Hamas caused a shock by winning the majority of seats in the polls, which were seen by some as the most transparent to be held in the Palestinian territories.