Palestinian Prime Minister Ismail Haniya "called Central Elections Commission chief Hanna Nasser and invited him to Gaza for talks about voter registration," a statement said.
Hamas and the rival Fatah movement have been taking tentative steps to restart long-stalled reconciliation efforts, seeking to implement an agreement signed in Cairo in 2011 that was intended to lead to new elections.
The deal called for the formation of an interim government of independents that would oversee preparations for legislative and presidential elections, including the updating of voter rolls in the Gaza Strip.
But disagreement on the make-up of the government has held up implementation of the deal, and the CEC has yet to begin work in the coastal territory.
Haniya's spokesman Taher al-Nunu said the invitation was extended "in the context of the application of understandings reached in Cairo, and we hope to move forward simultaneously on the other issues."
CEC spokesman Farid Toameh confirmed the conversation between Haniya and Nasser, saying the Prime Minister had stressed "his government had no objection to the commission beginning its work" in Gaza.
"The elections commission needs three weeks from the beginning of its work to bring the electoral rolls up to date across the Gaza Strip," he added, saying that Nasser would travel to Gaza on Sunday or Monday.
Earlier this month, Fatah's chief envoy on the reconciliation process Azzam al-Ahmed said a key to implementing the agreement would be the restart of the CEC's work by January 30.