Israeli Prime Minister Ariel Sharon has said he hopes to meet new Palestinian leader Mahmoud Abbas "soon".
Ariel Sharon says the first meeting will focus on security issues
He phoned Mr Abbas to congratulate him on his election victory, Israeli and Palestinian officials confirmed.
After his election was confirmed, the new Palestinian leader offered "the hand of peace" to Israel and said he wanted talks to resume.
Meanwhile, the Palestinian Authority has announced plans to reorganise Palestinian security forces.
The reforms - under which the number of security services will be cut from 11 to three -were long promised by Mr Abbas' predecessor Yasser Arafat, but never carried out.
Mr Sharon said his first meeting with Mr Abbas would focus on security issues.
Moderate head of main political faction Fatah
Seen as someone Israel will talk to
Willing to talk peace with Israel
Wants end to Palestinian armed uprising
Pledges to stick to key positions of late Yasser Arafat
The prime minister "congratulated him on his personal achievement and his victory in the elections and wished him luck", said a statement issued by Mr Sharon's office.
"They agreed they would continue talking in the near future."
The statement was released after Mr Sharon held his first cabinet meeting with his new Labour coalition partners.
Israeli security sources said Israel was prepared to allow Palestinians to resume the policing of most occupied areas, if Mr Abbas showed he was trying his utmost to control militants.
This could mean a halt on army raids and removal of checkpoints.
Mr Abbas has called for calm as he tries to prepare the ground for a return to the internationally backed "roadmap" peace plan.
But Palestinian militants launched new missile attacks on Israel and Jewish settlements in the Gaza Strip on Tuesday.
The rocket and mortar bomb attacks caused damage, but no casualties.
Mr Abbas is due to be sworn in as Palestinian president on Wednesday.
Final official results show he won 62.3% of Sunday's vote.