Søreide also met with Palestinian lead negotiator Saeb Erekat.
Following the meetings, the foreign minister told Norwegian broadcaster NRK that leaders in both Palestine and Israel want Norway to facilitate future peace talks between the two countries.
“Both Israeli and Palestinian leaders would like Norway to facilitate potential future peace talks,” she told NRK.
Søreide also stressed that the situation remains difficult and that she was realistic about the peace process.
The minister was speaking after meeting with Erekat, but before she spoke to Abbas on Monday.
“Norway has helped us before, so we trust you,” Erekat told NRK.
Søreide also said that she believed there was “a willingness to resume processes and discussion, including with the Americans.”
The Norwegian foreign minister met with Israel's prime minister Benjamin Netanyahu on Sunday.
“I think we should be cautious, but I can see the will to find answers [to problems],” she told newspaper Dagsavisen after that meeting.
Both Abbas and Erekat have criticised US president Donald Trump's decision to recognise Jerusalem as Israel's capital.
“It [the decision by Trump] is the worst strategic decision any American president has made,” Erekat said Monday according to news agency NTB.
But Søreide said that the Palestinians would nevertheless have to consider an expected forthcoming peace plan from Washington, D.C.
“The United States will probably present its peace plan in a few months' time, and the parties must then consider that, whether they like it or not,” she told Dagsavisen after the meeting with Netanyahu.
No mention of Norway potentially facilitating peace talks between Palestine and Israel was made immediately following the meeting with the Israeli PM.
The Scandinavian country hosted the peace talks that led to 1993's Oslo Accord between the Government of Israel and the Palestine Liberation Organization.