Speaking at the swearing in of new MPs at the parliament building in the West Bank town of Ram Allah, the Palestinian leader said the next government must recognise existing peace agreements and commit to peace negotiations as the "sole ... strategic choice" of the Palestinians.
Abbas also came down hard on Israel, which has said it will not negotiate with a Hamas administration.
"We totally reject (Israel's) unilateral approach and exhort the peace-loving world, namely the quartet and American administration, to make serious, immediate efforts to restart negotiations on the basis of the signed agreements, namely Oslo and the roadmap," he said.
New Hamas MP Ismail Haniya, the man widely tipped to be the next prime minister, said his party had political differences with Abbas but that they would be "resolved by dialogue".
However, another Hamas spokesman rejected Abbas' calls for talks with Israel.
Mushir al-Masri said negotiations with Israel were "not on our agenda".
Abbas offered his help and encouragement in the speedy creation of a new administration.
Hamas is expected to nominate
Haniya as the next PM
He said the Hamas victory in last month's parliament election - and the defeat of his own Fatah Party - had led to new political reality.
"Therefore, it (Hamas) will be asked to form the new government," Abbas told Saturday's opening session.
The swearing-in follows Hamas's sensational victory last month over Abbas' Fatah party, winning 74 seats to Fatah's 45.
Hamas MPs in the Gaza Strip participated in the inauguration ceremony via video link-up, because Israel had banned them from travelling to the West Bank.
Nearly 2000 diplomats and other VIPs gathered in a government complex to view the parliament session, along with about 100 women from the Hamas Women's Union, their faces covered by veils.
The new parliament is only the second legislature to be inaugurated since 1994.
Proceedings were briefly disturbed when about 100 policemen staged an angry protest outside the building demanding the payment of delayed salaries.
Hamas is widely expected to nominate Haniya as prime minister. He is one of the movement's Gaza-based leaders and considered a pragmatic radical by many.
Aziz al-Duwaik, a geography professor from the southern West Bank city of Hebron, has already been chosen as the speaker of parliament.
Hamas, deemed a terrorist organisation by the United States and several other Western nations, has called for the destruction of Israel.
The 132-seat parliament is only
the second sworn in since 1994
Horrified at the prospect of what it considers a terrorist government, Israel is expected to greet the new parliament by approving a series of sanctions directed at restricting Palestinian residents, goods and finances.
One possible move is an immediate freeze on the transfer of customs duties collected by Israel on Palestinians' behalf - about $50 million a month or about one-third of the Palestinian Authority's annual budget.
Haniya has already lambasted the plans as a "policy of repression, terrorism and collective punishment against our people."