Swedish relations with Israel sank to an all-time low after the Nordic country's center-left government decided in October to recognize Palestine, just weeks after it took office.
Foreign Minister Margot Wallstroem - who last month postponed a trip to Israel - has said she will use the Abbas visit to "prepare for a revived peace process".
"It's of course not about being the most central actor in potential peace talks," political scientist Ann-Marie Ekengren at Gothenburg University told AFP.
"But perhaps Wallstroem sees Sweden's role as a facilitator which sets the stage for future negotiations."
Last Friday, Wallstrom said she would press Abbas to include women in efforts to build a viable Palestinian state.
Wallstrom said she believes that after Sweden in October became the first European Union member to recognize Palestinian statehood, "we will have their ear." She said world reaction to the move, although criticized by Israel, was overwhelmingly positive, adding that it wasn't about "being against Israel, it is about being for peace."
Abbas' visit - his first to Sweden since 2009 - comes a month after a senior Israeli official said Wallstroem was not welcome for official visits to the country.
"It does not make us happy to see (Abbas) here on a visit with a new government that very quickly decided to recognize Palestine," Israel's ambassador to Stockholm Isaac Bachman told news agency TT.
According to the Palestinian Authority, around 135 countries have recognized the state of Palestine including several that are now EU members.
Peace talks between Israel and the Palestinians collapsed in April last year, and a bloody conflict in Gaza erupted just a few months later.
In December, a United Nations report accusing Sweden of violating human rights of refugees, minors and minorities served as a basis for a diplomatic settling of scores between Stockholm and Jerusalem.
"It turns out that the state of human and children's rights in a country that is sharply critical of us on the same issues, particularly regarding the territories, is much less glorious than could be expected," commented Israeli Ambassador to Sweden Isaac Bachman.
In January, Wallstrom canceled her trip to Israel after she was notified that she would have to bring her own security personnel and that her trip would not be considered an official state visit.
Itamar Eichner contributed to this report.