Mahmoud Abbas has been sworn in as the new Palestinian president at a ceremony in the West Bank town of Ramallah.
Abbas is facing tough challenges amid a surge in violence
Mr Abbas used his inauguration speech to call for a ceasefire between Israel and Palestinian militants.
As the ceremony took place, Israeli troops killed six Palestinians, while militants seriously injured an Israeli child in a rocket attack in Gaza.
Israel has severed contacts with the Palestinians after militants killed six Israelis in the Gaza Strip on Thursday.
Meanwhile, dozens of Palestinian election officials resigned on Saturday, alleging irregularities and intimidation in Sunday's presidential election.
The Central Elections Commission officials who quit said they were coerced into extending voting hours by security personnel and campaigners loyal to Mr Abbas, Reuters news agency reported.
In the latest violence, six Palestinians - some armed - were killed in two separate clashes with Israeli forces in the Gaza Strip.
The army said four Palestinians died after its troops came under fire in Gaza City, while two Palestinians were killed in Rafah near the Egyptian border.
At least one Israeli child was seriously hurt when a mortar shell fired by militants hit Netzarim settlement in northern Gaza.
Paramedics said the child lost an arm in the attack.
In his inaugural speech, Mr Abbas called for an end to the violence.
"We condemn these actions, whether by the Israeli occupation forces or the reactions of some Palestinian factions," he said.
"This does not help bring about the calm needed to enable a credible, serious peace process. We are seeking a mutual ceasefire to end this vicious circle."
He went on to call for talks on a final peace deal, saying: "Our hand is extended toward an Israeli partner for making peace."
But he made no mention of the crackdown on militants demanded by Israel.
Back to square one?
After his election, Israeli Prime Minister Ariel Sharon called Mr Abbas to congratulate him and said he hoped to meet the new leader "soon".
Violence continued in Gaza as Mr Abbas was sworn in
But by Friday hopes for a speedy meeting appeared to be dashed.
"Israel informed international leaders today that there will be no meetings with Abbas until he makes a real effort to stop the terror," Mr Sharon's spokesman Assaf Shariv said.
A Palestinian cabinet minister, Saeb Erekat, protested.
"We call on the Israelis to resume a meaningful peace process and dialogue because this is the only way to break the vicious cycle of violence," Mr Erekat said.
The BBC's James Reynolds, in Jerusalem, says that the inauguration day offers a rare moment for some Palestinian ceremony after years of uprising and violence.
But with Mr Abbas cut off by the Israelis, as Yasser Arafat was before him, the Palestinians find that they are in some ways right back to where they were before, our correspondent says.