Swedish relations with Israel sank to an all-time low after the Nordic country's centre-left government decided in October to recognise 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."
Signup to our newsletter and follow us on Facebook and Twitter!
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 recognise Palestine," Israel's ambassador to Stockholm Isaac Bachman told news agency TT.
Sweden is the only major western European country to have recognised Palestine.
According to the Palestinian Authority, around 135 countries have recognised 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 war in Gaza erupted just a few months later.