"We do not underestimate the difficulties for us or for the parties," Mitchell said, following his meeting with Abbas.
"But we all have obligations to do everything we can to help achieve the goal of comprehensive peace that will be good for the Palestinians, good for the Israelis, good for all the people in this region."
Mitchell said that Israeli and Palestinian envoys had been invited to continue their consultations in Washington.
Saeb Erekat, the chief Palestinian negotiator, said that he could see those talks taking place "maybe in the next two weeks".
'Peace impossible'
Israeli-Palestinian peace talks were broken off late last year after Ehud Olmert, Netanyahu's predecessor, resigned amid corruption allegations, sending Israel into early elections that saw Netanyahu return to power after 10 years.
The Palestinians have insisted on a complete freeze of Israeli construction in the occupied West Bank before the peace process can resume.
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"I will tell him [Mitchell] clearly: there are many conflicts in the world that haven't reached a comprehensive solution and people have learned to live with this"
Avigdor Lieberman, Israel's foreign minister
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Mitchell and his aides are expected to meet a team of Netanyahu aides for continued talks on Saturday.
But Israel has not shown any signs of willingness to halt construction and Mitchell's latest visit to the region is a fresh attempt to revive the talks.
Avigdor Lieberman, Israel's foreign minister, said on Thursday that he would tell Mitchell a comprehensive peace deal between Israel and the Palestinians was impossible, and that an interim deal was his preferred option.
"Whoever says that it's possible to reach in the coming years a comprehensive agreement that means the end of conflict, that both sides sign up to the end of conflict, simply does not understand the reality," he told Israel Radio.
"I will tell him [Mitchell] clearly: there are many conflicts in the world that haven't reached a comprehensive solution and people have learned to live with this," he said, citing continuing land disputes in Cyprus, Nagorno-Karabakh and the Falkland Islands.
Mitchell's last visit to the region in September failed to seal a deal on the settlement freeze.
'Disappointment'
Al Jazeera's Sherine Tadros, reporting from Jerusalem, said: "Mitchell had a lot of momentum when he first started coming, [but] this is his sixth, seventh time in the region and he has yet to bring anything on the ground and changes in terms of bigger policy.
"People here are very upset and angry and becoming increasingly disappointed with this new US approach, which is briging nothing new to the table in terms of changes that Palestinians can actually see going on."
A three-way summit between Netanyahu, Abbas and Barack Obama, the US president, went ahead in New York in September without the US being able to announce a revival of the talks.
Obama announced instead that the three parties would begin intense contacts in a bid to revive the talks later this autumn, possibly by late October.