Adwan was allowed into the country in the face of protests from Israel and France to attend a conference on Palestinian exiles.
“I will visit four countries,” Adwan told news agency AFP on Tuesday after meeting with Swedish lawmakers despite a European Union policy of no contact with the movement.
Sweden and 14 other European countries have agreed, under the so-called Schengen accord, that a visa delivered by any of them is valid for all others.
The other Schengen countries are Austria, Belgium, Denmark, Finland, France, Germany, Iceland, Italy, Greece, Luxembourg, Netherlands, Norway, Portugal and Spain.
Adwan declined to say which four countries he was planning to visit before his visa expires on May 16.
The granting of a Swedish visa to Adwan sparked a strong protest from Israel, which said the decision “helped legitimize a terrorist organization.”
On Tuesday Israeli embassy spokeswoman Ann Ringart told AFP that the Swedish stance was damaging the Middle East peace process.
“Granting a visa to a minister in the Hamas government is bringing us 20 years back in the peace process instead of furthering it,” she said.
Hamas is listed as a terrorist organization by the EU and the United States, which have suspended direct aid to the government.
France has also implicitly criticized the decision to grant a visa to the Hamas minister, saying it would have intervened with the Swedish government if it had had advance notice of Adwan’s application.
But Adwan said on Tuesday that his successful visa application meant that EU countries had “started to actually change” their hardline position towards Hamas.
“Because when they allowed me to come, they gave me a Schengen visa. According to this visa I am allowed to go through all the European countries.
This is what I will do. I will visit many countries, some of them invited me semi-officially, and that’s good news,” he said.
Since his arrival in Sweden, Edwane has thanked Sweden for allowing him into the country, and emphasized his hope for dialogue with EU countries.
The Swedish government has said none of its members would meet with Hamas representatives.