Bildt will hold talks with Palestinian president and Fatah chief Mahmud Abbas, as well as independent cabinet members such as Foreign Minister Ziad Abu Amr and Finance Minister Salam Fayyad, he said.
But ministers from the dominant Hamas group, which is regarded as a terrorist organization in Israel and the West, would not be consulted.
Hamas swept to power a year ago but has been shunned by the European Union and the United States for its refusal to recognise Israel and its use of tactics such as suicide bombings.
Most direct foreign aid to the government was ended, including a crippling Israeli boycott which drove the Palestinian Authority into bankruptcy.
On Monday, the United States and European Union agreed to withhold recognition of the unity government grouping Western-backed moderates and Islamic radicals, but they did leave the door open to future ties.
Along with the United Nations and Russia, which make up the Middle East diplomatic Quartet, they insist that the cabinet recognise Israel, renounce violence and respect past peace agreements.
EU officials have agreed that the EU’s position on dealing with the government — at least non-Hamas members in it — is likely to be formalised at a meeting of the bloc’s foreign ministers in Germany late next week.
Bildt is also expected to fly to Israel at the weekend to meet Israeli Foreign Minister Tzipi Livni, his spokesman said.